# Fundamental Theorem of Calculus – Exercise 2382

Exercise

Given the function

$$f(x):R\rightarrow R$$

The function is continuous and differential. The following holds

$$f(2)=3, f(6)=\frac{1}{2}, f'(2)=5$$

Calculate the derivative of the function

$$g(x)=\int_0^{x f(x)} f(t)dt$$

At the point x=2.

$$g'(2)=6\frac{1}{2}$$