The fifth derivative $\frac { d ^ { 5 } } { d x ^ { 5 } } \left( 5 x ^ { 4 } - e ^ { x } \right)$ is

A) $60 x ^ { 3 } - e ^ { x }$
B) $180 x ^ { 2 } - e ^ { x }$
C) $360 x - e ^ { x }$
D) $360 - e ^ { x }$
E) $- e ^ { x }$

Question

The fifth derivative $\frac { d ^ { 5 } } { d x ^ { 5 } } \left( 5 x ^ { 4 } - e ^ { x } \right)$ is

A) $60 x ^ { 3 } - e ^ { x }$
B) $180 x ^ { 2 } - e ^ { x }$
C) $360 x - e ^ { x }$
D) $360 - e ^ { x }$
E) $- e ^ { x }$

Quizplus · Accepted Answer

The polynomial term $5x^4$ becomes zero after the fourth derivative, and the derivative of $-e^x$ remains $-e^x$ for all orders.

The Fifth Derivative d5dx5(5x4−ex)\frac { d ^ { 5 } } { d x ^ { 5 } } \left( 5 x ^ { 4 } - e ^ { x } \right)dx5d5​(5x4−ex)