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

Identify components: Identify the function components to apply the product rule: f(x) = g(x)h(x), where g(x) = cos(x) and h(x) = x^(-2).Apply product rule: Apply the product rule: f'(x) = g'(x)h(x) + g(x)h'(x).Calculate g'(x): Calculate g'(x): g'(x) = -sin(x).Calculate h'(x): Calculate h'(x): h'(x) = -2x^(-3).Plug in values: Plug in g'(x) and h'(x) into the product rule: f'(x) = (-sin(x))(x^(-2)) + (cos(x))(-2x^(-3)).Simplify expression: Simplify the expression: f'(x) = -sin(x)/x^2 - 2cos(x)/x^3.Combine terms: Combine the terms: f'(x) = (-sin(x)x - 2cos(x))/x^3.

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

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Algebra 1

Write variable expressions for arithmetic sequences

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Q. Let

f(x)=\cos (x) x^{-2}

\newline

f^{\prime}(x)=

Identify components: Identify the function components to apply the product rule: $f(x) = g(x)h(x)$ , where $g(x) = \cos(x)$ and $h(x) = x^{-2}$ .
Apply product rule: Apply the product rule: $f'(x) = g'(x)h(x) + g(x)h'(x)$ .
Calculate $g'(x)$ : Calculate $g'(x)$ : $g'(x) = -\sin(x)$ .
Calculate $h'(x)$ : Calculate $h'(x)$ : $h'(x) = -2x^{-3}$ .
Plug in values: Plug in $g'(x)$ and $h'(x)$ into the product rule: $f'(x) = (-\sin(x))(x^{-2}) + (\cos(x))(-2x^{-3})$ .
Simplify expression: Simplify the expression: $f'(x) = -\frac{\sin(x)}{x^2} - \frac{2\cos(x)}{x^3}$ .
Combine terms: Combine the terms: $f'(x) = \frac{-\sin(x)x - 2\cos(x)}{x^3}$ .