Question

What is the implicit derivative of `10=ye^y-x^2+ye^x`?

Answer 1

`(dy)/(dx)=(2x-ye^x)/((1+y)e^y+e^x)`

Explanation:

Implicit differentiation of `10=ye^y-x^2+ye^x` is

`0=(dy)/(dx)e^y+ye^y(dy)/(dx)-2x+(dy)/(dx)e^x+ye^x`

`(dy)/(dx)=(2x-ye^x)/(e^y+ye^y+e^x)=(2x-ye^x)/((1+y)e^y+e^x)`