Question

use implicit differentiation to solve: xy = sinx + siny

Answer 1

use the product rule and chain rule. anything involving y's uses t he chain rule

\(\frac{d}{dx}y=\frac{dy}{dx}=y'\)

Answer 2

so start with the left hand side
xy=?

Answer 3

recall uv = u'v+uv'

Answer 4

\(\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)\)

Answer 5

final answer I came up with is dy/dx = (cosx - y)/(x - cosy)

Answer 6

wolfram disagrees with my answer

Answer 7

it likes mine

Answer 8

wolfram pls :(

Answer 9

are both correct?

Answer 10

I don't think mine's correct but this makes a pretty graph http://www.wolframalpha.com/input/?i=%28cosx+-+y%29%2F%28x+-+cosy%29%3D%28y-cosx%29%2F%28x%2Bcosy%29

honestly, go with wolfram it's more likely to be correct than mine. I have to relook at whatI did wrong