Question

Calculate following derivatives:
\[\Large \frac{d}{dx} \int_0^{x^{2}} dt \frac{\exp t}{t^{2}+1}\]

Answer 1

do you know how to find the derivative of an integration?

Answer 2

not really first yesterday night i have looked a little bit how interal functions, thats all.

Answer 3

I know i need to use this here..
\[\Large \frac{d}{dx} \int\limits_{a(x)}^{b(x)} f(t) dt= f(b(x)) \ b'(x)- f(a(x)) \ a'(x)\]

Answer 4

yep. that straight away gives the answer right?

Answer 5

i dont know how to apply it... it would be much appreciate if you can solve it, naturally if you can..

Answer 6

see the function \[f(t)=e^{t}/(t^{2}+1)\]
and a(x)=0, so naturally a'(x)=0
and b(x)=x^2 and so b'(x)=2x
\[f(b(x))=e^{x^{2}}/(x^{4}+1)\] and f(a(x))=f(0)=1. substitute them to get the answer.

Answer 7

ok i will try thanks...