Question

if $f(x)=\frac{3}{x^{2}}$, find $f(5)$.

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{3}{x^{2}}$ as $f(x)=3x^{- 2}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y'=anx^{n - 1}$. For $f(x)=3x^{-2}$, we have $f'(x)=3\times(-2)x^{-2 - 1}=-6x^{-3}=-\frac{6}{x^{3}}$.

Step3: Evaluate $f'(5)$

Substitute $x = 5$ into $f'(x)$. So $f'(5)=-\frac{6}{5^{3}}=-\frac{6}{125}$.

Answer:

$-\frac{6}{125}$