# Homework Help: Implicit Differentiation problem

1. Jul 9, 2007

### suxatphysix

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

Find dy/dx by implicit differentiation when it is known that y^2 + xsiny = 4

2. Relevant equations

3. The attempt at a solution

2y dy/dt + xcosy dy/dt + siny = 0

2y dy/dt + xcosy dy/dt = -siny

dy/dt + dy/dt = -siny/2y/xcosy

I'm sure I'm doing it wrong so I stopped right there. What am I doing it wrong and how do I solve it?

Thanks

2. Jul 9, 2007

### bob1182006

you're looking for dy/dx not dy/dt o.o, but assuming by dt you mean dx then in the 2nd line of your attempt you should pull out the dy/dt and the answer will be easy from there.

3. Jul 9, 2007

### suxatphysix

dy/dx = -siny/2y+xcosy

4. Jul 9, 2007

### Dick

It would be if you would parenthesize the denominator.

5. Jul 9, 2007

### suxatphysix

dy/dx = -siny/(2y+xcosy) ? What's that's do

6. Jul 9, 2007

### Dick

It distinguishes between -(siny/(2y))+(xcosy) and -siny/(2y+xcosy). Which are two quite different expressions. But look the same if you omit the parentheses.

Last edited: Jul 9, 2007
7. Jul 9, 2007

### Fizix

$$\frac{d}{dx}(y^2+x\sin(y)) = 0$$

$$=2y\left(\frac{dy}{dx}\right)+\left[\frac{d}{dx}x\cdot\sin(y)+\frac{d}{dx}\sin(y)\cdot x\right]=0$$

$$= 2y\left(\frac{dy}{dx}\right) + \left[\sin(y) + x\cdot\cos(y)\left(\frac{dy}{dx}\right)\right]= 2y\left(\frac{dy}{dx}\right) + \sin(y) + x\cos(y)\left(\frac{dy}{dx}\right) = 2y\left(\frac{dy}{dx}\right) + x\cos(y)\left(\frac{dy}{dx}\right) + \sin(y) = 0$$

$$= \left(\frac{dy}{dx}\right)(2y+x\cos(y)) + \sin(y) = 0$$

$$= \left(\frac{dy}{dx}\right)(2y+x\cos(y)) = -\sin(y)$$

$$\left(\frac{dy}{dx}\right) = \frac{-\sin(y)}{(2y+x\cos(y))}$$

Edit: I'm late by about 25 minutes.

8. Jul 9, 2007

cool thanks