# Homework Help: Implici differentiation

1. Jul 6, 2008

### jkeatin

1. The problem statement, all variables and given/known data

dy/dx: square root x+y= 1+x^3y^2

2. Relevant equations

chain rule
implicit differentiation

3. The attempt at a solution

1/2 x+y -1/2 =2x^2y^3 *y'

Last edited: Jul 6, 2008
2. Jul 6, 2008

### rocomath

$$\sqrt{x+y}=1+x^3y^2$$

Be clear!!! Make use of parenthesis. Right?

3. Jul 6, 2008

4. Jul 6, 2008

### jkeatin

1/2(x+y)^-1/2(x+y)'= (2x^2y^2)(y)'(x^3)

5. Jul 6, 2008

### jkeatin

am i going in the right direction?

6. Jul 6, 2008

### rock.freak667

To differentiate the LHS w.r.t x
1/2(x+y)^-1/2 is correct but you'll need to multiply it by the differential of (x+y) i.e. what is in the bracket.

For the RHS : $1+x^3y^2$ use the product law for $x^3y^2$

7. Jul 6, 2008

### jkeatin

ok
1/2(x+y)^-1/2 + 1/2(x+y)^-1/2 (y)'= 3x^2y^2 +2y (y)' (x^3)

8. Jul 6, 2008

### jkeatin

is that right?

9. Jul 6, 2008

### Defennder

Yes it is.

10. Jul 6, 2008

### jkeatin

do i need to simplify anymore?

11. Jul 6, 2008

### Defennder

Are you required to?

12. Jul 6, 2008

### jkeatin

I need to find y'

13. Jul 6, 2008

### jkeatin

y'= 3x^2-1/2(x+y)^-1/2 over [1/2(x+y)^-1/2] - 2yx^3

14. Jul 6, 2008

### rocomath

Defennder confirmed your "Calculus steps" I'm sure you can handle the rest.