Compute the derivative of the given function below

Question

f(x)=₀∫^{x^3}e^-tdt

df/dx=?

Answer 1

f(x) = ∫_{(from 0 to x^3)} e^-tdt

df/dx = e^{-x^3} [d/dx(x³)] = e^{-x^3}(3x²) = 3x²e^{-x^3}