Question

find f(x) if f(x) = (6x + 4)^2.
f(x) = □

Explanation:

Step1: Apply chain - rule

Let $u = 6x + 4$, then $f(x)=u^{2}$. The chain - rule states that $f^{\prime}(x)=\frac{df}{du}\cdot\frac{du}{dx}$.

Step2: Differentiate $f$ with respect to $u$

$\frac{df}{du}=\frac{d}{du}(u^{2}) = 2u$

Step3: Differentiate $u$ with respect to $x$

$\frac{du}{dx}=\frac{d}{dx}(6x + 4)=6$

Step4: Substitute $u$ back and find $f^{\prime}(x)$

$f^{\prime}(x)=\frac{df}{du}\cdot\frac{du}{dx}=2u\times6$. Substituting $u = 6x + 4$ back in, we get $f^{\prime}(x)=2(6x + 4)\times6=12(6x + 4)=72x+48$

Answer:

$72x + 48$