Let g(x)=x^(-10). g^(')(1)=

Apply Power Rule: To find the derivative of g(x) = x^(-10), we need to use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1). So, we will apply this rule to g(x).Calculate Derivative: Applying the power rule to g(x) = x^(-10), we get g'(x) = -10*x^(-10-1) = -10*x^(-11).Substitute x=1: Now we need to evaluate the derivative at x=1. So we substitute x with 1 in the expression for g'(x) to get g'(1) = -10*1^(-11).Evaluate g'(1): Since any non-zero number to the power of -11 is just its reciprocal, 1^(-11) is simply 1. Therefore, g'(1) = -10*1 = -10.

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Algebra 2

Simplify variable expressions using properties

Full solution

Q. Let

g(x)=x^{-10}

\newline

g^{\prime}(1)=

Apply Power Rule: To find the derivative of $g(x) = x^{-10}$ , we need to use the power rule for differentiation, which states that the derivative of $x^n$ with respect to $x$ is $n \cdot x^{n-1}$ . So, we will apply this rule to $g(x)$ .
Calculate Derivative: Applying the power rule to $g(x) = x^{-10}$ , we get $g'(x) = -10 \cdot x^{-10-1} = -10 \cdot x^{-11}$ .
Substitute $x=1$ : Now we need to evaluate the derivative at $x=1$ . So we substitute $x$ with $1$ in the expression for $g'(x)$ to get $g'(1) = -10\cdot1^{-11}$ .
Evaluate $g'(1)$ : Since any non-zero number to the power of $-11$ is just its reciprocal, $1^{(-11)}$ is simply $1$ . Therefore, $g'(1) = -10 \times 1 = -10$ .