Question

question 7
if $f(x)=\frac{1}{x^2}$, find $f(1)$.
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Explanation:

Step1: Rewrite function for differentiation

Rewrite $f(x)=\frac{1}{x^2}$ as $f(x)=x^{-2}$

Step2: Apply power rule for derivatives

The power rule states $\frac{d}{dx}[x^n]=nx^{n-1}$. For $n=-2$:
$f'(x)=-2x^{-2-1}=-2x^{-3}=-\frac{2}{x^3}$

Step3: Evaluate at $x=1$

Substitute $x=1$ into $f'(x)$:
$f'(1)=-\frac{2}{1^3}$

Answer:

$-2$