Question

find f(x).
f(x)=(6 - 7x)^{14}
f(x)=□

Explanation:

Step1: Identify the outer - function and inner - function

Let $u = 6-7x$, so $y = u^{14}$.

Step2: Differentiate the outer - function

Using the power rule $\frac{d}{du}(u^n)=nu^{n - 1}$, for $y = u^{14}$, $\frac{dy}{du}=14u^{13}$.

Step3: Differentiate the inner - function

For $u = 6-7x$, $\frac{du}{dx}=-7$.

Step4: Apply the chain rule

The chain rule states that $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $\frac{dy}{du}=14u^{13}$ and $\frac{du}{dx}=-7$ into the chain - rule formula. Replace $u$ with $6 - 7x$.
$\frac{dy}{dx}=14(6 - 7x)^{13}\cdot(-7)$.

Step5: Simplify the result

$\frac{dy}{dx}=-98(6 - 7x)^{13}$.

Answer:

$-98(6 - 7x)^{13}$