What is the value of (d)/(dx)(x^(-7)) at x=-1 ?

Apply Power Rule: We need to find the derivative of the function f(x) = x^(-7) with respect to x. To do this, we use the power rule for differentiation, which states that if f(x) = x^n, then f'(x) = n*x^(n-1).Calculate Derivative: Applying the power rule to f(x) = x^(-7), we get f'(x) = (-7)*x^(-7-1) = -7*x^(-8).Substitute x = -1: Now we need to evaluate the derivative at x = -1. So we substitute x with -1 in the expression for f'(x): f'(-1) = -7*(-1)^(-8).Evaluate Derivative: Since any non-zero number raised to an even power is positive, (-1)^(-8) is equal to 1. Therefore, f'(-1) = -7*1 = -7.We have found the value of the derivative at x = -1, which is -7. This completes the problem.

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What is the value of
(d)/(dx)(x^(-7)) at
x=-1 ?

What is the value of $\frac{d}{d x}\left(x^{-7}\right)$ at $x=-1$ ?

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Precalculus

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Q. What is the value of

\frac{d}{d x}\left(x^{-7}\right)

x=-1

Apply Power Rule: We need to find the derivative of the function $f(x) = x^{-7}$ with respect to $x$ . To do this, we use the power rule for differentiation, which states that if $f(x) = x^n$ , then $f'(x) = n \cdot x^{n-1}$ .
Calculate Derivative: Applying the power rule to $f(x) = x^{-7}$ , we get $f'(x) = (-7)\cdot x^{-7-1} = -7\cdot x^{-8}$ .
Substitute $x = -1$ : Now we need to evaluate the derivative at $x = -1$ . So we substitute $x$ with $-1$ in the expression for $f'(x)$ : $f'(-1) = -7*(-1)^{-8}$ .
Evaluate Derivative: Since any non-zero number raised to an even power is positive, $(-1)^{-8}$ is equal to $1$ . Therefore, $f'(-1) = -7\cdot1 = -7$ .
Evaluate Derivative: Since any non-zero number raised to an even power is positive, $(-1)^{-8}$ is equal to $1$ . Therefore, $f'(-1) = -7\times1 = -7$ .We have found the value of the derivative at $x = -1$ , which is $-7$ . This completes the problem.