(d)/(dx)((1)/(x^(8)))=

Apply Power Rule: To find the derivative of the function (1)/(x^(8)) 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^(8)) as x^(-8).Calculate Derivative: Applying the power rule, we take the exponent -8 and multiply it by the function, then subtract 1 from the exponent to get the new power of x. So the derivative of x^(-8) is -8*x^(-8-1) which simplifies to -8*x^(-9).Final Form: The expression -8*x^(-9) can be rewritten as -8/(x^9) for clarity, which is the final form of the derivative.

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Algebra 2

Simplify variable expressions using properties

Full solution

\frac{d}{d x}\left(\frac{1}{x^{8}}\right)=

Apply Power Rule: To find the derivative of the function $\frac{1}{x^{8}}$ 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 $\frac{1}{x^{8}}$ as $x^{-8}$ .
Calculate Derivative: Applying the power rule, we take the exponent $-8$ and multiply it by the function, then subtract $1$ from the exponent to get the new power of $x$ . So the derivative of $x^{-8}$ is $-8\cdot x^{-8-1}$ which simplifies to $-8\cdot x^{-9}$ .
Final Form: The expression $-8x^{-9}$ can be rewritten as $-\frac{8}{x^9}$ for clarity, which is the final form of the derivative.