Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x^n sin x

Question

n=1 f'(x)=

n=2 f'(x)=

n=3 f'(x)=

n=4 f'(x)=

Use the results to write a general rule for f '(x)

 in terms of n.

f'(x)=

Answer 1

xⁿ cos x + nx^n-1 sin x