Find the derivative of the following function. $y = 5 e ^ { 3 x ^ { 2 } - 3 }$
A) $y ^ { \prime } = 15 x e ^ { 3 x ^ { 2 } - 3 }$
B) $y ^ { \prime } = 30 x e ^ { 3 x ^ { 2 } - 3 }$
C) $y ^ { \prime } = 30 e ^ { 3 x ^ { 2 } - 3 }$
D) $y ^ { \prime } = 15 e ^ { 3 x ^ { 2 } - 3 }$
E) $y ^ { \prime } = 10 x e ^ { 3 x ^ { 2 } - 3 }$

Question

Quizplus · Accepted Answer

To find the derivative of $y = 5e^{3x^2 - 3}$, we use the chain rule. The derivative of $e^{3x^2 - 3}$ with respect to $x$ is $e^{3x^2 - 3} \cdot 6x$, because the derivative of $3x^2 - 3$ with respect to $x$ is $6x$. Therefore, $y' = 5 \cdot 6x \cdot e^{3x^2 - 3} = 30x e^{3x^2 - 3}$.

Find the Derivative of the Following Function y=5e3x2−3y = 5 e ^ { 3 x ^ { 2 } - 3 }y=5e3x2−3

Find the Derivative of the Following Function $y = 5 e ^ { 3 x ^ { 2 } - 3 }$