Find the derivative.
-$\frac { d } { d x } \int _ { 0 } ^ { x ^ { 4 } } \sin t d t$
A) $\frac { 1 } { 5 } x ^ { 5 } \sin \left( x ^ { 4 } \right)$
B) $\sin \left( x ^ { 4 } \right)$
C) $- \cos \left( x ^ { 4 } \right) - 1$
D) $4 x ^ { 3 } \sin \left( x ^ { 4 } \right)$

Question

Quizplus · Accepted Answer

By the Fundamental Theorem of Calculus, we have 
$$\frac { d } { d x } \int _ { 0 } ^ { x ^ { 4 } } \sin t d t = \sin (x^4) \cdot \frac{d}{dx} x^4 = 4x^3 \sin (x^4).$$
Thus, the answer is (D).

Find the Derivative ddx∫0x4sin⁡tdt\frac { d } { d x } \int _ { 0 } ^ { x ^ { 4 } } \sin t d tdxd​∫0x4​sintdt

Find the Derivative $\frac { d } { d x } \int _ { 0 } ^ { x ^ { 4 } } \sin t d t$