overall accuracy: 84.7% accuracy last 50: 86% record: 42 score: 41 d/dx (e^3x) = 3e^3x -1/3e^3x e^3x 1/3e^3x…

Explanation:

Step1: Recall chain - rule

The chain - rule for differentiation is $\frac{d}{dx}(f(g(x)))=f'(g(x))\cdot g'(x)$. For $y = e^{3x}$, let $u = 3x$, then $y = e^{u}$.

Step2: Differentiate outer and inner functions

The derivative of $y = e^{u}$ with respect to $u$ is $\frac{dy}{du}=e^{u}$, and the derivative of $u = 3x$ with respect to $x$ is $\frac{du}{dx}=3$.

Step3: Apply chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substituting $\frac{dy}{du}=e^{u}$ and $\frac{du}{dx}=3$ and $u = 3x$ back in, we get $\frac{dy}{dx}=3e^{3x}$.

Answer:

$3e^{3x}$