How do you differentiate #cos(x) = x/(x-y^2-y)#?

1 Answer
Bdub
Feb 29, 2016

#(x-y^2-y)cosx=x, xcosx-y^2cosx-ycosx=x#
#d/dx(xcosx-y^2cosx-ycosx=x)#
#-xsinx+cosx-(-y^2sinx+2ycosxdy/dx)-(-ysinx+dy/dxcosx)=1#
#dy/dx=(-xsinx+cosx+y^2sinx+ysinx-1)/(2ycosx+cos x)#

Explanation:

First multiply the denominator over to the other side and then distribute the cos x in. Then take the derivative of both sides and then put every term without dydx on one side and all the terms with dy/dx on the other side then solve for dy/dx.

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