Question

What is the derivate of...?

`sin(xy)+e^(xy)=e^x`

Answer 1

`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)))`