find the derivative $\displaystyle \frac{d}{dx}\int^a_x \tan(\tan(t))\,dt =$

Question

Find the derivative: $\displaystyle \frac{d}{dx}\int^a_x \tan(\tan(t))\,dt = $

I tried to take the derivative but I am getting the wrong answer every time.

Maybe you can show your work so we can see where it is going wrong. Regards — Amzoti, Dec 07 '13 at 01:35

score 3 · Answer 1 · answered Dec 07 '13 at 01:37

3

Make use of the fundamental theorem of calculus: $$\dfrac{d}{dx}\left(\int_a^x f(t) dt \right) = f(x)$$

answered Dec 07 '13 at 01:37

score 2 · Answer 2 · answered Dec 07 '13 at 01:44

2

Hints: (1) Fundamental Theorem of Calculus and (2) $\int_b^a f(x)\,dx=-\int_a^b f(x)\,dx$

answered Dec 07 '13 at 01:44

JohnD

2 Answers2