The functions are and
.
Consider .
Fundamental theorem of calculus :
\If is continuous on
, then the function
is defined by
is continuous on
and differentiable on
, then
.
From the fundamental theorem of calculus, part 1:
\.
Therefore, .
Consider .
Consider .
Differentiate on each side with respect to .
.
Apply derivative on each side with respect to .
Rewrite the expression using chain rule.
\.
.
From the fundamental theorem of calculus, part 1:
\.
Here .
.
Replace and
in above expression.
.
We have, .
Substitute in above expression.
.
.