Question

hw8 defining the derivative (targets l6, d3; §3.1)
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if ( f(x)=\frac{4}{x^{2}} ), find ( f(5) ).
basic funcs trig
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Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{4}{x^{2}}$ as $f(x) = 4x^{- 2}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y'=anx^{n - 1}$. For $f(x)=4x^{-2}$, we have $f'(x)=4\times(-2)x^{-2 - 1}=-8x^{-3}=-\frac{8}{x^{3}}$.

Step3: Evaluate $f'(x)$ at $x = 5$

Substitute $x = 5$ into $f'(x)$. So $f'(5)=-\frac{8}{5^{3}}=-\frac{8}{125}$.

Answer:

$-\frac{8}{125}$