Use the Fundamental Theorem of Calculus to carry out the following differentiation:

Question

Use the Fundamental Theorem of Calculus to carry out the following differentiation:

d ∫₁√x t^t dt= ?

dx

integral from 1 to sqrt x

Answer 1

d/dx[√x] = 1/(2√x) so d/dx[∫...] = 1/(2√x) · (√x)^√x = (√x)^{√x - 1} / 2 or .5x^1/2(√x-1)