Let h(x)=x^(-5). h^(')(2)=

Identify Function & Point: Identify the function and the point at which we need to find the derivative. The function given is h(x) = x^(-5), and we need to find the derivative of h at x = 2, denoted as h'(2).Differentiate with Respect: Differentiate the function h(x) with respect to x. The derivative of x^n with respect to x is n*x^(n-1). Therefore, the derivative of h(x) = x^(-5) is h'(x) = -5*x^(-5-1) = -5*x^(-6).Substitute x = 2: Substitute x = 2 into the derivative to find h'(2). h'(2) = -5*(2)^(-6) = -5 / (2^6).Calculate h'(2): Calculate the value of h'(2). 2^6 = 64, so h'(2) = -5 / 64.

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Let $h(x)=x^{-5}$ . $\newline$ $h^{\prime}(2)=$

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Algebra 1

Write and solve inverse variation equations

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Q. Let

h(x)=x^{-5}

\newline

h^{\prime}(2)=

Identify Function & Point: Identify the function and the point at which we need to find the derivative. The function given is $h(x) = x^{-5}$ , and we need to find the derivative of $h$ at $x = 2$ , denoted as $h'(2)$ .
Differentiate with Respect: Differentiate the function $h(x)$ with respect to $x$ . The derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ . Therefore, the derivative of $h(x) = x^{-5}$ is $h'(x) = -5\cdot x^{(-5-1)} = -5\cdot x^{-6}$ .
Substitute $x = 2$ : Substitute $x = 2$ into the derivative to find $h'(2)$ . $\newline$ $h'(2) = -5\cdot(2)^{-6} = -5 / (2^6)$ .
Calculate $h'(2)$ : Calculate the value of $h'(2)$ . $2^6 = 64$ , so $h'(2) = -\frac{5}{64}$ .