Question

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

Answer 1

\[
2x\frac {e^{x^2}}{x^4+1}
\]

Answer 2

FTC and Chain Rule

Answer 3

Mr Saab is it end solution so that i can write it tomorrow on exam if same question appears?

Answer 4

yes

Answer 5

\[
\frac {d}{dx}\int_{v(x)}^{u(x)} f(x)dx = f(u(x)) u'(x)- f(v(x)) v'(x)
\]

Answer 6

In your case
\[
v(x)=0\\
u(x)=x^2
\]

Answer 7

ok thank you very very much mr Saab

Answer 8

\[\frac {d}{dx}\int_{v(x)}^{u(x)} f(t)dt = f(u(x)) u'(x)- f(v(x)) v'(x)\]
A small misprint

Answer 9

ok thank you