Identify Function: We are asked to find the derivative of the function x^(-9) with respect to x. To do this, we will use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).Apply Power Rule: Applying the power rule to x^(-9), we differentiate as follows: d/dx(x^(-9)) = -9*x^(-9-1). This is because we bring down the exponent as a coefficient and subtract one from the exponent.Simplify Expression: Simplify the expression: -9*x^(-9-1) = -9*x^(-10).

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

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Algebra 2

Simplify variable expressions using properties

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

Identify Function: We are asked to find the derivative of the function $x^{-9}$ with respect to $x$ . To do this, we will use the power rule for differentiation, which states that the derivative of $x^n$ with respect to $x$ is $n*x^{n-1}$ .
Apply Power Rule: Applying the power rule to $x^{-9}$ , we differentiate as follows: $\frac{d}{dx}(x^{-9}) = -9\cdot x^{-9-1}$ . This is because we bring down the exponent as a coefficient and subtract one from the exponent.
Simplify Expression: Simplify the expression: $-9x^{(-9-1)} = -9x^{-10}.$