Question

How do you differentiate `f(x)=e^(x^2+x+8)` using the chain rule?

Answer 1

`d/dx (e^(x^2+x+8)) = (2x+1)e^(x^2+x+8)`

Explanation:

Based on the chain rule, let `y(x) = x^2+x+8`, then:

`(df)/dx = (df)/dy dy/dx = d/dy (e^y) * d/dx (x^2+x+8)`

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

`(df)/dx = (df)/dy dy/dx = (2x+1)e^(x^2+x+8)`