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Mathematics 17 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

yep. that straight away gives the answer right?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

ok i will try thanks...

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