Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Question

h(x) = ∫e^x1 9 ln(t) dt

Answer 1

First h(x) = ∫ from e^x to 9 of ln(t)dt = - ∫from 9 to e^x of lntdt;

By 1 fundamental theorem of calculus we have h'(x) = - ln(e^x)·(e^x)' = - x·e^x;

Answer: h'(x) = - x·e^x;