For the equation given, evaluate y′ at the point (−2,−1) [closed]
$begingroup$
I must find the derivative for this equation
$$
(3x−y)^4+4y^3=621
$$
at the point $(-2,-1)$.
calculus implicit-differentiation
edited Jan 24 at 20:49
gt6989b
34.7k22456
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
$endgroup$
closed as off-topic by T. Bongers, Dietrich Burde, Abcd, Alexander Gruber♦ Jan 24 at 23:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – T. Bongers, Dietrich Burde, Abcd, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I must find the derivative for this equation
$$
(3x−y)^4+4y^3=621
$$
at the point $(-2,-1)$.
calculus implicit-differentiation
edited Jan 24 at 20:49
gt6989b
34.7k22456
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
$endgroup$
closed as off-topic by T. Bongers, Dietrich Burde, Abcd, Alexander Gruber♦ Jan 24 at 23:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – T. Bongers, Dietrich Burde, Abcd, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Have you tried anything yet?
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:49
$begingroup$
Yes. Taking the derivative and plugging in for x and y values
$endgroup$
– Caroline Arns
Jan 24 at 20:52
$begingroup$
Ok, then maybe you should append your question to include what you tried and then we can tell you whether it is correct or not.
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:54
add a comment |
$begingroup$
I must find the derivative for this equation
$$
(3x−y)^4+4y^3=621
$$
at the point $(-2,-1)$.
calculus implicit-differentiation
edited Jan 24 at 20:49
gt6989b
34.7k22456
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
$endgroup$
I must find the derivative for this equation
$$
(3x−y)^4+4y^3=621
$$
at the point $(-2,-1)$.
calculus implicit-differentiation
calculus implicit-differentiation
edited Jan 24 at 20:49
gt6989b
34.7k22456
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
edited Jan 24 at 20:49
gt6989b
34.7k22456
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
edited Jan 24 at 20:49
gt6989b
34.7k22456
edited Jan 24 at 20:49
gt6989b
34.7k22456
edited Jan 24 at 20:49
gt6989b
34.7k22456
34.7k22456
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
asked Jan 24 at 20:47
Caroline ArnsCaroline Arns
6
6
closed as off-topic by T. Bongers, Dietrich Burde, Abcd, Alexander Gruber♦ Jan 24 at 23:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – T. Bongers, Dietrich Burde, Abcd, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by T. Bongers, Dietrich Burde, Abcd, Alexander Gruber♦ Jan 24 at 23:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – T. Bongers, Dietrich Burde, Abcd, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Have you tried anything yet?
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:49
$begingroup$
Yes. Taking the derivative and plugging in for x and y values
$endgroup$
– Caroline Arns
Jan 24 at 20:52
$begingroup$
Ok, then maybe you should append your question to include what you tried and then we can tell you whether it is correct or not.
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:54
add a comment |
$begingroup$
Have you tried anything yet?
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:49
$begingroup$
Yes. Taking the derivative and plugging in for x and y values
$endgroup$
– Caroline Arns
Jan 24 at 20:52
$begingroup$
Ok, then maybe you should append your question to include what you tried and then we can tell you whether it is correct or not.
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:54
$begingroup$
Have you tried anything yet?
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:49
$begingroup$
Have you tried anything yet?
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:49
$begingroup$
Yes. Taking the derivative and plugging in for x and y values
$endgroup$
– Caroline Arns
Jan 24 at 20:52
$begingroup$
Yes. Taking the derivative and plugging in for x and y values
$endgroup$
– Caroline Arns
Jan 24 at 20:52
$begingroup$
Ok, then maybe you should append your question to include what you tried and then we can tell you whether it is correct or not.
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:54
$begingroup$
Ok, then maybe you should append your question to include what you tried and then we can tell you whether it is correct or not.
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:54
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
With some differential calculus: differentiating both sides you obtain:
$$4(3x-y)^3(3,mathrm dx -mathrm dy)+12 y^2,mathrm dy=0$$
which becomes for $x=-2,;y=-1$:
$$-500(3,mathrm dx -mathrm dy)+12 ,mathrm dy=0iff 512,mathrm dy=1500,mathrm dxifffrac{mathrm dy}{mathrm dx}=frac{1500}{512}=frac{375}{128}.$$
answered Jan 24 at 21:07
BernardBernard
122k741116
$endgroup$
add a comment |
$begingroup$
HINT
- Differentiate both sides (use Chain Rule carefully). You should get two terms with $y'$ and one term without $y'$ on the LHS and 0 on the RHS.
- Solve for $y'$.
- Plug in your point $x = -2,y=-1$.
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
$endgroup$
add a comment |
$begingroup$
Use $$left((3x-y)^4+4y^3right)'=0.$$
We obtain $$4(3x-y)^3(3-y')+12y^2y'=0.$$
Can you end it now?
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
$endgroup$
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
With some differential calculus: differentiating both sides you obtain:
$$4(3x-y)^3(3,mathrm dx -mathrm dy)+12 y^2,mathrm dy=0$$
which becomes for $x=-2,;y=-1$:
$$-500(3,mathrm dx -mathrm dy)+12 ,mathrm dy=0iff 512,mathrm dy=1500,mathrm dxifffrac{mathrm dy}{mathrm dx}=frac{1500}{512}=frac{375}{128}.$$
answered Jan 24 at 21:07
BernardBernard
122k741116
$endgroup$
add a comment |
$begingroup$
With some differential calculus: differentiating both sides you obtain:
$$4(3x-y)^3(3,mathrm dx -mathrm dy)+12 y^2,mathrm dy=0$$
which becomes for $x=-2,;y=-1$:
$$-500(3,mathrm dx -mathrm dy)+12 ,mathrm dy=0iff 512,mathrm dy=1500,mathrm dxifffrac{mathrm dy}{mathrm dx}=frac{1500}{512}=frac{375}{128}.$$
answered Jan 24 at 21:07
BernardBernard
122k741116
$endgroup$
add a comment |
$begingroup$
With some differential calculus: differentiating both sides you obtain:
$$4(3x-y)^3(3,mathrm dx -mathrm dy)+12 y^2,mathrm dy=0$$
which becomes for $x=-2,;y=-1$:
$$-500(3,mathrm dx -mathrm dy)+12 ,mathrm dy=0iff 512,mathrm dy=1500,mathrm dxifffrac{mathrm dy}{mathrm dx}=frac{1500}{512}=frac{375}{128}.$$
answered Jan 24 at 21:07
BernardBernard
122k741116
$endgroup$
With some differential calculus: differentiating both sides you obtain:
$$4(3x-y)^3(3,mathrm dx -mathrm dy)+12 y^2,mathrm dy=0$$
which becomes for $x=-2,;y=-1$:
$$-500(3,mathrm dx -mathrm dy)+12 ,mathrm dy=0iff 512,mathrm dy=1500,mathrm dxifffrac{mathrm dy}{mathrm dx}=frac{1500}{512}=frac{375}{128}.$$
answered Jan 24 at 21:07
BernardBernard
122k741116
answered Jan 24 at 21:07
BernardBernard
122k741116
answered Jan 24 at 21:07
BernardBernard
122k741116
answered Jan 24 at 21:07
BernardBernard
122k741116
122k741116
add a comment |
add a comment |
$begingroup$
HINT
- Differentiate both sides (use Chain Rule carefully). You should get two terms with $y'$ and one term without $y'$ on the LHS and 0 on the RHS.
- Solve for $y'$.
- Plug in your point $x = -2,y=-1$.
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
$endgroup$
add a comment |
$begingroup$
HINT
- Differentiate both sides (use Chain Rule carefully). You should get two terms with $y'$ and one term without $y'$ on the LHS and 0 on the RHS.
- Solve for $y'$.
- Plug in your point $x = -2,y=-1$.
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
$endgroup$
add a comment |
$begingroup$
HINT
- Differentiate both sides (use Chain Rule carefully). You should get two terms with $y'$ and one term without $y'$ on the LHS and 0 on the RHS.
- Solve for $y'$.
- Plug in your point $x = -2,y=-1$.
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
$endgroup$
HINT
- Differentiate both sides (use Chain Rule carefully). You should get two terms with $y'$ and one term without $y'$ on the LHS and 0 on the RHS.
- Solve for $y'$.
- Plug in your point $x = -2,y=-1$.
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
answered Jan 24 at 20:51
gt6989bgt6989b
34.7k22456
34.7k22456
add a comment |
add a comment |
$begingroup$
Use $$left((3x-y)^4+4y^3right)'=0.$$
We obtain $$4(3x-y)^3(3-y')+12y^2y'=0.$$
Can you end it now?
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
$endgroup$
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
add a comment |
$begingroup$
Use $$left((3x-y)^4+4y^3right)'=0.$$
We obtain $$4(3x-y)^3(3-y')+12y^2y'=0.$$
Can you end it now?
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
$endgroup$
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
add a comment |
$begingroup$
Use $$left((3x-y)^4+4y^3right)'=0.$$
We obtain $$4(3x-y)^3(3-y')+12y^2y'=0.$$
Can you end it now?
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
$endgroup$
Use $$left((3x-y)^4+4y^3right)'=0.$$
We obtain $$4(3x-y)^3(3-y')+12y^2y'=0.$$
Can you end it now?
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
answered Jan 24 at 20:52
Michael RozenbergMichael Rozenberg
107k1895199
107k1895199
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
add a comment |
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
I got y'=497/11
$endgroup$
– Caroline Arns
Jan 24 at 21:02
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
maybe I am missing a step I just solved it like any other "solve for variable" equation.
$endgroup$
– Caroline Arns
Jan 24 at 21:08
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
$begingroup$
I got $y'(-2,-1)=frac{375}{128}.$
$endgroup$
– Michael Rozenberg
Jan 24 at 21:12
add a comment |
$begingroup$
Have you tried anything yet?
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:49
$begingroup$
Yes. Taking the derivative and plugging in for x and y values
$endgroup$
– Caroline Arns
Jan 24 at 20:52
$begingroup$
Ok, then maybe you should append your question to include what you tried and then we can tell you whether it is correct or not.
$endgroup$
– Jack Pfaffinger
Jan 24 at 20:54