Question

differentiate. f(x)=(4x + 5)^2 f(x)=□

Explanation:

Step1: Apply chain - rule

Let $u = 4x + 5$, then $F(x)=u^{2}$. The chain - rule states $\frac{dF}{dx}=\frac{dF}{du}\cdot\frac{du}{dx}$.
$\frac{dF}{du} = 2u$ and $\frac{du}{dx}=4$.

Step2: Substitute $u$ back

Substitute $u = 4x + 5$ into $\frac{dF}{du}\cdot\frac{du}{dx}$.
$F^{\prime}(x)=2(4x + 5)\cdot4$.

Step3: Simplify

$F^{\prime}(x)=8(4x + 5)=32x+40$.

Answer:

$32x + 40$