Let f(x)=x^(-2). f^(')(2)=

Apply Power Rule: We need to find the derivative of the function f(x) = x^(-2) with respect to x. To do this, we will use the power rule for differentiation, which states that if f(x) = x^n, then f^(')(x) = n*x^(n-1).Calculate Derivative: Applying the power rule to f(x) = x^(-2), we get f^(')(x) = (-2)*x^(-2-1) = -2*x^(-3).Substitute x=2: Now we need to evaluate the derivative at x = 2. So we substitute x with 2 in the expression for f^(')(x) to get f^(')(2) = -2*(2)^(-3).Evaluate f'(2): Calculating the value of f^(')(2), we have f^(')(2) = -2*(1/2^3) = -2*(1/8) = -2/8.Simplify Fraction: Simplifying the fraction -2/8, we get f^(')(2) = -1/4.

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Let $f(x)=x^{-2}$ . $\newline$ $f^{\prime}(2)=$

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Q. Let

f(x)=x^{-2}

\newline

f^{\prime}(2)=

Apply Power Rule: We need to find the derivative of the function $f(x) = x^{-2}$ with respect to $x$ . To do this, we will use the power rule for differentiation, which states that if $f(x) = x^n$ , then $f^{\prime}(x) = n \cdot x^{n-1}$ .
Calculate Derivative: Applying the power rule to $f(x) = x^{-2}$ , we get $f^{\prime}(x) = (-2)\cdot x^{-2-1} = -2\cdot x^{-3}$ .
Substitute $x=2$ : Now we need to evaluate the derivative at $x = 2$ . So we substitute $x$ with $2$ in the expression for $f^{\prime}(x)$ to get $f^{\prime}(2) = -2\cdot(2)^{-3}$ .
Evaluate $f'(2)$ : Calculating the value of $f'(2)$ , we have $f'(2) = -2\times\left(\frac{1}{2^3}\right) = -2\times\left(\frac{1}{8}\right) = -\frac{2}{8}$ .
Simplify Fraction: Simplifying the fraction $-\frac{2}{8}$ , we get $f^{\prime}(2) = -\frac{1}{4}$ .