Find $\frac{d}{d x} \int_{0}^{x}\left(\cos \left(t^{4}\right)+\sin \left(t^{4}\right)\right) d t$ .
A) $\cos \left(x^{4}\right)+\sin \left(x^{4}\right)$
B) $\sin \left(x^{4}\right)-\cos \left(x^{4}\right)$
C) $\sin \left(4 x^{3}\right)-\cos \left(4 x^{3}\right)$
D) $\frac{x^{5}}{5}\left(\sin \left(x^{4}\right)-\cos \left(x^{4}\right)\right)$

Question

Quizplus · Accepted Answer

The derivative of the integral from a constant to x of a function is just the function itself evaluated at x, according to the Fundamental Theorem of Calculus.

Find ddx∫0x(cos⁡(t4)+sin⁡(t4))dt\frac{d}{d x} \int_{0}^{x}\left(\cos \left(t^{4}\right)+\sin \left(t^{4}\right)\right) d tdxd​∫0x​(cos(t4)+sin(t4))dt A) cos⁡(x4)+sin⁡(x4)\cos \left(x^{4}\right)+\sin \left(x^{4}\right)cos(x4)+sin(x4)

Find $\frac{d}{d x} \int_{0}^{x}\left(\cos \left(t^{4}\right)+\sin \left(t^{4}\right)\right) d t$
A) $\cos \left(x^{4}\right)+\sin \left(x^{4}\right)$