What is the derivate of...?

sin(xy)+e^(xy)=e^xsin(xy)+exy=ex

1 Answer
Jun 12, 2018

y'= (e^x-y(cosx(xy)+e^(xy)))/(x(cosx(xy)+e^(xy)))

Explanation:

Differentiate both sides of the equation:

d/dx (sin(xy)+e^(xy)) = d/dx e^x

(y+xy')cosx(xy)+(y+xy')e^(xy) = e^x

y(cosx(xy)+e^(xy)) +xy'(cosx(xy)+e^(xy)) = e^x

Solve now for y':

y'= (e^x-y(cosx(xy)+e^(xy)))/(x(cosx(xy)+e^(xy)))