Question

Let f(x) = (1-t^2)^1/3 from the integral 1 to cosx. Find and simplify f'(x)

Answer 1

would it be correct to replace t with cos x and then multiply with derivative?

Answer 2

or am I mistaking that process for if it was integral 0 to cos x

Answer 3

Use the fundamental theorem of calculus:
\[\frac{d}{dx}\left[\int_c^{g(x)}f(t)~dt\right]=f(g(x))\cdot g'(x)\]
where \(c\) is a constant.

Answer 4

oh gotcha tysm