# Thread: Need help with quesiton - derivative and riemann's sum

1. ## Need help with quesiton - derivative and riemann's sum

i'm not really sure how to do this questions b/c of the notations :S if som1 could instruct me on understanding and getting started that would be great, thx

2. ## Re: Need help with quesiton - derivative and riemann's sum

Originally Posted by simba412
finding the derivative with respect to x...
2x
3t2 9 dt.
x
i'm not really sure how to do this questions b/c of the notations :S if som1 could instruct me on understanding and getting started that would be great

Is the question to find the derivative of $\int_x^{2x } {\left( {3t^2 - 9} \right)dt}$ with respect to $x~?$

If so, suppose that each of $f~\&~g$ is a differentiable function and $y = \int_{g(x)}^{f(x)} {h(t)dt}$ then $y' = f'(x)h(f(x)) - g'(x)h(g(x))$

3. ## Re: Need help with quesiton - derivative and riemann's sum

the upper limit is 2x. yes i think its (3t^2 -9)dt... although it is written as 3t^2 - 9 dt (exactly as in the posted pic)....

4. ## Re: Need help with quesiton - derivative and riemann's sum

Originally Posted by simba412
the upper limit is 2x. yes i think its (3t^2 -9)dt... although it is written as 3t^2 - 9 dt (exactly as in the posted pic)....
That does not in anyway change my answer.
Actually from a mathematical viewpoint, the notation in that image is extremely poor.

The answer is $(2)[3(2x)^2-9]-(1)[3(x)^2-9]$

5. ## Re: Need help with quesiton - derivative and riemann's sum

yes i got that. thanks for the reply. thats mostly why i got confused, i feel there should be brackets around the fn't ...