Let h(x)=(1)/(x^(6)). h^(')(1)=

Differentiate function h(x): Differentiate the function h(x) = 1/x^6 with respect to x. To differentiate h(x), we 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 h(x) as x^(-6) and then apply the power rule. h'(x) = d/dx [x^(-6)] h'(x) = -6*x^(-6-1) h'(x) = -6*x^(-7)Apply power rule: Evaluate the derivative at x = 1. We substitute x = 1 into the derivative we found in Step 1. h'(1) = -6*1^(-7) h'(1) = -6*1^(-7) Since any number to the power of -7 is just its reciprocal raised to the 7th power, and the reciprocal of 1 is still 1, we have: h'(1) = -6*(1) h'(1) = -6

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Let $h(x)=\frac{1}{x^{6}}$ . $\newline$ $h^{\prime}(1)=$

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Q. Let

h(x)=\frac{1}{x^{6}}

\newline

h^{\prime}(1)=

Differentiate function $h(x)$ : Differentiate the function $h(x) = \frac{1}{x^6}$ with respect to $x$ . To differentiate $h(x)$ , we 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 $h(x)$ as $x^{-6}$ and then apply the power rule. $h'(x) = \frac{d}{dx} [x^{-6}]$ $h(x) = \frac{1}{x^6}$ $0$ $h(x) = \frac{1}{x^6}$ $1$
Apply power rule: Evaluate the derivative at $x = 1$ . We substitute $x = 1$ into the derivative we found in Step $1$ . $h'(1) = -6 \cdot 1^{-7}$ $h'(1) = -6 \cdot 1^{-7}$ Since any number to the power of $-7$ is just its reciprocal raised to the $7$ th power, and the reciprocal of $1$ is still $1$ , we have: $h'(1) = -6 \cdot (1)$ $h'(1) = -6$