Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $$h ( x ) = \int _ { 1 } ^ { \sqrt { x } } \frac { z ^ { 2 } } { z ^ { 4 } + 1 } d z$$
A) $\frac { \sqrt { x + 1 } } { x ^ { 2 } + 2 }$
B) $\frac { \sqrt { x ^ { 2 } + 1 } } { 2 }$
C)
$\frac { \sqrt { x } } { 2 \left( x ^ { 2 } + 1 \right) }$
D) $\frac { \sqrt { x } } { x ^ { 2 } + 1 }$
E) none of these

Question

Quizplus · Accepted Answer

The derivative of the integral with respect to $x$ is found using the chain rule and the Fundamental Theorem of Calculus, resulting in $\frac{\sqrt{x}}{2(x^2 + 1)}$.

Use Part 1 of the Fundamental Theorem of Calculus to Find