Need to make sure I'm getting this right
Is
$\displaystyle A) \frac{d}{dx}\int_3^{e{^x^2}} ln(t^3) dt=2x^3e^x^2
$
and
$\displaystyle B) \frac{d}{dx}\int_a^x \frac{f(t}{t^2}=\frac{-2f(x)}{x}$
Need to make sure I'm getting this right
Is
$\displaystyle A) \frac{d}{dx}\int_3^{e{^x^2}} ln(t^3) dt=2x^3e^x^2
$
and
$\displaystyle B) \frac{d}{dx}\int_a^x \frac{f(t}{t^2}=\frac{-2f(x)}{x}$
It is not clear what the integrand function and limits are.
$\displaystyle B) \frac{d}{dx}\int_a^x \frac{f(t}{t^2}=\frac{-2f(x)}{x}$
$\displaystyle \dfrac{d}{dx}\displaystyle\int_a^x \dfrac{f(t)}{t^2}dt=\dfrac{f(x)}{x^2}$
Fernando Revilla
Using the Fundamental Theorem of Calculus an the Chain's Rule:
$\displaystyle \dfrac{d}{dx}\displaystyle\int_a^{g(x)} f(t)dt=f[g(x)]g'(x)$
Let us see what do you obtain.
Fernando Revilla