Let h(x)=(1)/(x^(11)). h^(')(x)=

Rewrite function: We are asked to find the derivative of the function h(x) = 1/(x^(11)). To do this, we will use the power rule for derivatives, which 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 h(x) = x^(-11) to apply the power rule.Apply power rule: Applying the power rule to h(x) = x^(-11), we get: h^(')(x) = (-11) * x^((-11) - 1) This simplifies to: h^(')(x) = -11 * x^(-12)Simplify derivative: We can rewrite the derivative in a more conventional form by moving the x term to the denominator: h^(')(x) = -11 / x^(12) This is the simplified form of the derivative of the function h(x).

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Let $h(x)=\frac{1}{x^{11}}$ . $\newline$ $h^{\prime}(x)=$

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Algebra 1

Multiplication with rational exponents

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Q. Let

h(x)=\frac{1}{x^{11}}

\newline

h^{\prime}(x)=

Rewrite function: We are asked to find the derivative of the function $h(x) = \frac{1}{x^{11}}$ . To do this, we will use the power rule for derivatives, which 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 $h(x) = x^{-11}$ to apply the power rule.
Apply power rule: Applying the power rule to $h(x) = x^{-11}$ , we get: $\newline$ $h^{\prime}(x) = (-11) \times x^{(-11) - 1}$ $\newline$ This simplifies to: $\newline$ $h^{\prime}(x) = -11 \times x^{-12}$
Simplify derivative: We can rewrite the derivative in a more conventional form by moving the $x$ term to the denominator: $h^{'}(x) = -\frac{11}{x^{12}}$ This is the simplified form of the derivative of the function $h(x)$ .