(d)/(dx)((1)/(x^(9)))=

Rewrite function: To find the derivative of the function (1)/(x^(9)) with respect to x, we will use the power rule for derivatives. The power rule states that the derivative of x^n with respect to x is n*x^(n-1). In this case, we can rewrite (1)/(x^(9)) as x^(-9).Apply power rule: Applying the power rule, we take the exponent -9 and multiply it by the function, then subtract 1 from the exponent to get the new power. So the derivative of x^(-9) is -9*x^(-9-1) or -9*x^(-10).Simplify expression: Simplify the expression -9*x^(-10) to get the final answer. Since x^(-10) is the same as 1/x^(10), the final derivative is -9/(x^(10)).

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Algebra 2

Simplify variable expressions using properties

Full solution

\frac{d}{d x}\left(\frac{1}{x^{9}}\right)=

Rewrite function: To find the derivative of the function $\frac{1}{x^{9}}$ with respect to $x$ , we will use the power rule for derivatives. The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{n-1}$ . In this case, we can rewrite $\frac{1}{x^{9}}$ as $x^{-9}$ .
Apply power rule: Applying the power rule, we take the exponent $-9$ and multiply it by the function, then subtract $1$ from the exponent to get the new power. So the derivative of $x^{-9}$ is $-9\cdot x^{-9-1}$ or $-9\cdot x^{-10}$ .
Simplify expression: Simplify the expression $-9x^{-10}$ to get the final answer. Since $x^{-10}$ is the same as $1/x^{10}$ , the final derivative is $-9/(x^{10})$ .