Derivative of e^(x^n)?

Question

what is the derivative of e^(x^n)?

Answer 1

Use the chain rule and let u = x^n, y=e^u

dy/du = e^u

du/dx = (n) x^(n-1)

dy/dx = (dy/du)(du/dx)

dy/dx = e^u (n) x^(n-1)

d/dx e^(x^n) = (n)x^(n-1)e^(x^n)

Answer: (n)x^(n-1)e^(x^n)

Answer 2

Firstly the derivative of e^x is e^x but in this case we have x^n rather than just plain x so we then need to use the chain rule. The derivative of x^n is nx^(n-1) so we get that the derivative of e^(x^n) is:

e^(x^n) * nx^(n-1)