Using the fundamental theorem of calculus, find the derivative of

F(x) = definite intergral from x=10 to x=x (tan theta)dtheta

steps please I've been trying to catch my mistake

Question

Using the fundamental theorem of calculus, find the derivative of

F(x) = definite intergral from x=10 to x=x (tan theta)dtheta

steps please I've been trying to catch my mistake

zarkon · Answer

there is like 1 step ;)

anonymous · Answer

$$d/dt\int tan\theta  d\theta=Log[cos[x]-Log[Cos[10]]]$$=  

d/dt   Log[Cos[x]]

anonymous · Answer

Tan[x]

zarkon · Answer

$$\frac{d}{dx}\int\limits_{a}^{x}f(\theta)d\theta=f(x)$$

zarkon · Answer

you have to be careful about what values of x works here

anonymous · Answer

Cos[10] is negative which makes the answer imaginary, so..

zarkon · Answer

it doesn't

also the answer is $\tan(x)$