Find the derivative of the function.
-$$z = 2 x ^ { 2 } e ^ { x }$$
A) $\frac { \mathrm { dz } } { \mathrm { dx } } = 4 x \mathrm { e } ^ { \mathrm { x } } - 2 \mathrm { x } ^ { 2 } \mathrm { e } ^ { \mathrm { x } }$
B) $\frac { d z } { d x } = 2 x e ^ { x } + 4 x ^ { 2 } e ^ { x }$
C) $\frac { d z } { d x } = 4 x e ^ { x } + 2 x ^ { 2 } e ^ { x }$
D) $\frac { d z } { d x } = 2 x e ^ { x } + 2 x ^ { 2 } e ^ { x }$

Question

Quizplus · Accepted Answer

We will use the product rule and chain rule for finding the derivative of the given function.

Let's start by applying the product rule:

$$\frac { d z } { d x } = 2 x ^ { 2 } \frac { d } { d x } e ^ { x } + e ^ { x } \frac { d } { d x } 2 x ^ { 2 }$$

Simplifying this expression using the chain rule of differentiation for $e^x$, we get:

$$\frac { d z } { d x } = 2x^2 e^x + 2xe^x.$$

Finally, simplifying this expression, we get:

$$\frac { d z } { d x } = 4x e ^ { x } + 2x^2 e^x.$$

Thus, the correct option is (C).

Find the Derivative of the Function z=2x2exz = 2 x ^ { 2 } e ^ { x }z=2x2ex

Find the Derivative of the Function $z = 2 x ^ { 2 } e ^ { x }$