Question

find the derivative f(x) = ∫_(√x)^2x▒arctan⁡〖t dt〗

Answer 1

i'm sorry but I really don't know what the f(x) is... could you please draw it or put it into equation form with the neat apps below?

Answer 2

\[\int\limits_{\sqrt{x}}^{2x} \arctan t dt\]

Answer 3

all it says is Find the derivative of the function and f(x)= above equation

Answer 4

use partial integration to find the antiderivative

Answer 5

If you need to find the derivative, then you don't need to integrate the function, you can use the fundamental theorem of calculus. Essentially the d/dx cancels out the integral, and you just plug in your limits as if you integrated, but you have to also multiply by the derivative of the limits.

\[\Large \frac{ d }{ dx } \int\limits\limits_{\sqrt{x}}^{2x} \arctan { t } dt = \frac{ d }{ dx }[2x]*\arctan 2x - \frac{ d }{ dx }[\sqrt x] * \arctan \sqrt {x} \]

All you have to do is differentiate the 2x and sqrtx.