# Thread: Finding the derivative of an intergral ...

1. ## Finding the derivative of an intergral ...

Hello,

I am trying to solve the problem below where I am attempting to find the derivative of an intergral. I tried the answer that is typed in but that is incorrect.

Any ideas? Thanks!

Regards,
Chris K.

2. Try $g'(x) = 3\left( {\frac{{3x + 2}}
{{3x - 4}}} \right) - 9\left( {\frac{{9x + 2}}
{{9x - 4}}} \right)$
.

3. Originally Posted by ckoeber
Hello,

I am trying to solve the problem below where I am attempting to find the derivative of an intergral. I tried the answer that is typed in but that is incorrect.

Any ideas? Thanks!

Regards,
Chris K.
No need for this hint, Just apply the following formula:
If $g(x)=\int_{m(x)}^{h(x)} f(u) du$ where m and h are differentiable functions.
then: $g'(x) = f(h(x)) h'(x) - f(m(x))m'(x)$.

$f(u)=\frac{u+2}{u-4}$.
$h(x)=3x$.
$m(x)=9x$.

4. Originally Posted by General
No need for this hint, Just apply the following formula:
If $g(x)=\int_{m(x)}^{h(x)} f(u) du$ where m and h are differentiable functions.
then: $g'(x) = f(h(x)) h'(x) - f(m(x))m'(x)$.

$f(u)=\frac{u+2}{u-4}$.
$h(x)=3x$.
$m(x)=9x$.
Thanks! This formula is awesome. Way better than the hint as I was my brain for 2 hours over this.

I got this:

Regards,
Chris K.