# How do you use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function  h(x) = 1/x int 2 arctan t dt?

Oct 22, 2015

If the intended function is $h \left(x\right) = {\int}_{x}^{1} 2 \arctan t \mathrm{dt}$, then see below.

#### Explanation:

Part 1 of the fundamental theorem of calculus tells us how to differentiate functions of the form

$g \left(x\right) = {\int}_{a}^{x} f \left(t\right) \mathrm{dt}$ for constant $a$

(We get $g ' \left(x\right) = f \left(x\right)$.)

The function $h$, in this question is not quite in the form we need, but we can rewrite it:

$h \left(x\right) = - {\int}_{1}^{x} 2 \arctan t \mathrm{dt}$

So, $h ' \left(x\right) = - 2 \arctan x$