if f'(x)=2(3x+5)^4 , then the fifth derivative of f(x) at x=-5/3 is

Question

A. 0
B. 144
C. 1,296
D. 3,888
E. 7,776

I got A

Answer 1

the 5th derivative of a 4th degree polynomial is zero.

But since they gave you f' rather than f, the 5th derivative of f is the 4th derivative of f'.

SO, f^(5) = 2*3^4 * 4! = 3888