Let y = $\mathrm { e } ^ { \mathrm { e } ^ { 2 x + 1 } }$ . What is $\frac { d y } { d x }$ ?
A) 2 $e ^ { 2 x + 1 }$
B) $\mathrm { e } ^ {e^{ 2 }}$
C) $e ^ { 2 }$
D) $e ^ { 2 x + 1 }$
E) none of these

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$, we use the chain rule. First, let $u = e^{2x + 1}$, so $y = e^u$. The derivative of $y$ with respect to $x$ is then found by differentiating $y$ with respect to $u$ and then multiplying by the derivative of $u$ with respect to $x$. This gives $\frac{dy}{dx} = e^u \cdot \frac{du}{dx} = e^{e^{2x+1}} \cdot 2e^{2x+1}$, which is not listed among the options provided.

Let Y = ee2x+1\mathrm { e } ^ { \mathrm { e } ^ { 2 x + 1 } }ee2x+1

Let Y = $\mathrm { e } ^ { \mathrm { e } ^ { 2 x + 1 } }$