Question

find the derivative of f(x).
f(x)=(-7x + 6)^2
f(x)=

Explanation:

Step1: Use the chain rule

The chain rule states that if \(y = u^n\) and \(u = g(x)\), then \(y^\prime=n\cdot u^{n - 1}\cdot g^\prime(x)\). Let \(u=-7x + 6\), \(n = 2\). First, find the derivative of the outer function. The derivative of \(u^{2}\) with respect to \(u\) is \(2u\).

Step2: Find the derivative of the inner function

The derivative of \(u=-7x + 6\) with respect to \(x\) is \(u^\prime=-7\).

Step3: Apply the chain rule

By the chain rule \(f^\prime(x)=2(-7x + 6)\times(-7)\).

Step4: Simplify the expression

$$
LATEXBLOCK0
$$

Answer:

\(f^\prime(x)=98x - 84\)