find the derivative of f(x).\nf(x)=(-7x + 6)^2\nf(x)=
find the derivative of f(x).\nf(x)=(-7x + 6)^2\nf(x)=
Answer
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
[ \begin{align*} f^\prime(x)&=2\times(-7)\times(-7x + 6)\ &=14\times(7x-6)\ &=98x-84 \end{align*} ]
Answer:
(f^\prime(x)=98x - 84)