Let f(x)=(1)/(x^(2)). f^(')(5)=

Apply Power Rule: To find the derivative of the function f(x) = 1/x^2, we need to apply the power rule for derivatives. The power rule states that the derivative of x^n with respect to x is n*x^(n-1). In this case, we can rewrite the function as f(x) = x^(-2) and then apply the power rule.Calculate Derivative: Applying the power rule, we get f'(x) = -2*x^(-2-1) = -2*x^(-3). This simplifies the derivative of the function to f'(x) = -2/x^3.Substitute x=5: Now we need to evaluate the derivative at x = 5. We substitute x with 5 in the derivative function f'(x) = -2/x^3 to get f'(5) = -2/5^3.Evaluate f'(5): Calculating the value of f'(5), we have f'(5) = -2/(5^3) = -2/125.

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Let $f(x)=\frac{1}{x^{2}}$ . $\newline$ $f^{\prime}(5)=$

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Algebra 2

Simplify variable expressions using properties

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Q. Let

f(x)=\frac{1}{x^{2}}

\newline

f^{\prime}(5)=

Apply Power Rule: To find the derivative of the function $f(x) = \frac{1}{x^2}$ , we need to apply the power rule for derivatives. The power rule states that the derivative of $x^n$ with respect to $x$ is $n \cdot x^{(n-1)}$ . In this case, we can rewrite the function as $f(x) = x^{-2}$ and then apply the power rule.
Calculate Derivative: Applying the power rule, we get $f'(x) = -2\cdot x^{(-2-1)} = -2\cdot x^{-3}$ . This simplifies the derivative of the function to $f'(x) = -\frac{2}{x^3}$ .
Substitute $x=5$ : Now we need to evaluate the derivative at $x = 5$ . We substitute $x$ with $5$ in the derivative function $f'(x) = -\frac{2}{x^3}$ to get $f'(5) = -\frac{2}{5^3}$ .
Evaluate $f'(5)$ : Calculating the value of $f'(5)$ , we have $f'(5) = -\frac{2}{(5^3)} = -\frac{2}{125}$ .