Question

How do you find the derivative of `e^y+e^xsin(y)=sin(xy)`?

Answer 1

`dy/dx=(ycos(xy)-e^xsiny)/(e^y +e^xcosy-xcos(xy))`

Explanation:

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

`e^y dy/dx+e^xsiny+e^xcosy dy/dx=ycos(xy)+xcos(xy)dy/dx`

`e^y dy/dx+e^xcosy dy/dx-xcos(xy)dy/dx=ycos(xy)-e^xsiny`

`dy/dx(e^y +e^xcosy-xcos(xy))=ycos(xy)-e^xsiny`

`dy/dx=(ycos(xy)-e^xsiny)/(e^y +e^xcosy-xcos(xy))`