Implicit Differentiation problem

[suxatphysix]

Homework Statement

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

Homework Equations

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

 

[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.

 

[suxatphysix]

Is this the answer?

dy/dx = -siny/2y+xcosy

 

[Dick]

It would be if you would parenthesize the denominator.

 

[suxatphysix]

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

 

[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.

 

[Fizix]

1. Homework Statement

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

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

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

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

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

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

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

Edit: I'm late by about 25 minutes.

 

[suxatphysix]

cool thanks