Find the derivative.
-$$y = \int _ { 0 } ^ { x } \frac { d t } { 2 t + 5 }$$
A) $\frac { 1 } { 2 x + 5 } - \frac { 1 } { 5 }$
B) $\frac { - 2 } { ( 2 x + 5 ) ^ { 2 } }$
C) $\frac { - 2 } { ( 2 x + 5 ) ^ { 2 } } + \frac { 2 } { 25 }$
D) $\frac { 1 } { 2 x + 5 }$

Question

Quizplus · Accepted Answer

By the fundamental theorem of calculus, if $y=\int_0^x \frac{dt}{2t+5}$, then $\frac{dy}{dx}=\frac{1}{2x+5}$. Therefore, the correct choice is D.

Find the Derivative y=∫0xdt2t+5y = \int _ { 0 } ^ { x } \frac { d t } { 2 t + 5 }y=∫0x​2t+5dt​

Find the Derivative $y = \int _ { 0 } ^ { x } \frac { d t } { 2 t + 5 }$