Question

find f(x).
f(x)=e^{7x}
f(x)=□

Explanation:

Step1: Identify the outer - inner functions

Let $u = 7x$, then $y = e^{u}$.

Step2: Differentiate the outer function

The derivative of $y = e^{u}$ with respect to $u$ is $\frac{dy}{du}=e^{u}$.

Step3: Differentiate the inner function

The derivative of $u = 7x$ with respect to $x$ is $\frac{du}{dx}=7$.

Step4: Apply the chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substituting $\frac{dy}{du}=e^{u}$ and $\frac{du}{dx}=7$ and $u = 7x$ back in, we get $\frac{dy}{dx}=e^{7x}\cdot7$.

Answer:

$7e^{7x}$