Posted by **Oli** on Monday, February 9, 2009 at 5:18am.

Hi,

I'm having trouble using implicit differentiation to determine dy/dx in the form dy/dx = f(x,y) for

sin(2x+3y)=3x^3y^2+4

Do I make it sin(2x+3y)-3x^3y^2=4 then differentiate to get

2cos(2x+3y)-9x^2*2y=0 ?

I'm a little lost...

Any help appreciated.

- Calculus -
**drwls**, Monday, February 9, 2009 at 6:00am
No. Your first step is IK but unecessary, and your second differentiation step is wrong.

Differentiate both sides of the equation with repect to x, remembering that y is a function of x. Use the "chain rule" when necessary.

cos(2x+3y)*(2 + 3dy/dx) = 6y^2x^2 +6x^3*y*dy/dx

Rearrange and solve for dy/dx

dy/dx[3cos(2x+3y)-6x^3 y]

= -2cos(2x+3y)- 6y^2x^2

One more step

- Calculus -
**Oli**, Monday, February 9, 2009 at 6:43am
Thanks for your reply.

I tried again and got

cos(2x+3y)*(2 + 3dy/dx = 9x^2y^2 + (6x^3*y dy/dx)

Looking at your answer it seems wrong also.

Should it not be 9y^2x^2... on the 1st part of the right hand side of your equation? Or am I missing something here?

Getting stuck on the rearranging but will it another try

- Calculus -
**drwls**, Monday, February 9, 2009 at 9:40am
Yes, it's 9x^2 y^2 where I had a coefficient of 6. Good work!

- Calculus -
**Oli**, Monday, February 9, 2009 at 4:32pm
Awesome. Think I've done it!

Cheers for the help.

## Answer this Question

## Related Questions

- Calculus - Use implicit differentiation to find dy/dx. e^4x = sin(x+2y). This is...
- Calculus - Find dy/dx of 3 sin x cos y = 2 using implicit differentiation.
- Calculus - Find dy/dx using implicit differentiation of xy + sin^2y=10350. Is it...
- Ap Calc AB - Determine (dy/dx) using implicit differentiation. cos(X^2Y^2) = x I...
- Calculus I - Find the derivative of f(x) = sin^2 (e^sin^2 x) I wonder if I'm ...
- Calculus - Find dy/dx for y=sin(x+y) A. 0 B. (cos(x+y))/(1-cos(x+y) C. cos(x+y) ...
- calculus - find y' by implicit differentiation: 5cos(x)*sin(y)=13
- calculus - Find dy/dx by implicit differentiation. sin x = x (1 + tan y)
- Calculus - How do you use imlicit differentiation to differentiate e^(xy)? I ...
- Math, derivatives - f(x) = x² + 2Cos²x, find f ' (x) a) 2(x+cos x) b) x - sin x ...