1. ## Definite Integral

If f(x) = ∫4x^3 (x^3 on top, 4 on bottom) t^5 ,

find f'(x)

find f'(4)

2. Originally Posted by derekjonathon
If f(x) = ∫4x^3 (x^3 on top, 4 on bottom) t^5 ,

find f'(x)

find f'(4)
You'll need to apply the FTC part 1:

$\frac{\,d}{\,dx}\left[\int_{a}^{g(x)}f\!\left(t\right)\,dt\right]=f\!\left(g\!\left(x\right)\right)\cdot g^{\prime}\!\left(x\right)$.

Can you take it from here?

3. ## I don't understand....

How the g(x) relates to the t^5dt part.....

how do I show a function of x^3 when I don't even see the variable (x) in the part that says t^5dt?

4. See attachment

5. ## I still can't figure the solution out...

It seems like it should be simple, but I'm just not getting it. How do I find f'(x)?

6. Originally Posted by derekjonathon
It seems like it should be simple, but I'm just not getting it. How do I find f'(x)?
You will need to post the integral in your question more clearly - it's clear that what we think it is is different to what you think it is.