## 1018 one year ago find y' : y=sin(x+y)

1. anonymous

You just have to differentiate both sides of the equation with respect to x $\frac{d}{dx}(y)=\frac{d}{dx}(\sin(x+y))$ Left side becomes simply derivative of y with respect to x, for the right side u must use chain rule Alternatively you can separate the variables $\sin^{-1}y=x+y$ $\sin^{-1}(y)-y=x$ Either way you'll have to differentiate both sides of the equation, you can't just reduce the equation into a form of $y=f(x)$ Such forms where you can't express y purely in terms of x are called as implicit, and we use implicit differentiation, in this method we simply differentiate the whole equation with respect to the independent variable and re arrange the dy/dx term

2. anonymous

Does that makes sense to you?

3. 1018

may i ask, is it always with respect to x? it says i need y'

4. anonymous

Generally it is with respect to x, most of the times you are required to find $y'=\frac{dy}{dx}$ Besides think about it, your equation only has 2 variables, x and y, so you can only find derivative of y with respect to x or with respect to y, derivative of y with respect to y would be 1 so that's kind of meaningless, so of course u have to find derivative of y with respect to x

5. anonymous

Anyways, try differentiation both sides of equation with respect to x, let's see where this gets you to

6. 1018

ok i think i got it. ill try again if my answer would be incorrect. thanks!

7. anonymous

Ok show me your work once you've attempted the question