Question

need to find derivative of an integral

Answer 1

\[ \frac{dy }{ dx} \int\limits_{\tan x}^{x ^{2}}\frac{ 1 }{ ?\sqrt{1+T ^{2}} } \]

Answer 2

ignore the "?"

Answer 3

\(\large \frac{dy }{ dx} \int\limits_{\tan x}^{x ^{2}}\frac{ 1 }{ \sqrt{1+T ^{2}} } dt = \frac{dy }{ dx} \int\limits_{\tan x}^{0}\frac{ 1 }{ \sqrt{1+T ^{2}} } dt + \frac{dy }{ dx} \int\limits_{0}^{x^2}\frac{ 1 }{ \sqrt{1+T ^{2}} } dt \)

Answer 4

use FTC + chain rule

Answer 5

thanks!