Find f ′(x) for f of x equals the integral from x cubed to 2 of the sine of t raised to the 4th power, dt.

In this question we have to find the derivative of F(x) which is

To find the derivative, our first step is to change the limits of the integral and on doing so , we have to put a minus sign , that is

Now we use fundamental law of calculus by substituting x^3 for t and we have to use chainrule too, that is

So the correct option is the last option .

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step-by-step explanation:

the answer is 62.8 cubic units