What is the value of (d)/(dx)(x^(-6)) at x=1 ?

Apply Power Rule: We need to find the derivative of the function f(x) = x^(-6) with respect to x. To do this, we will 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 our function, we get f'(x) = (-6)*x^(-6-1) = -6*x^(-7).Substitute x=1: Now we need to evaluate the derivative at x=1. So we substitute x with 1 in the derivative we found: f'(1) = -6*1^(-7).Evaluate f'(1): Since any non-zero number to the power of any real number is still that number, 1^(-7) is simply 1. Therefore, f'(1) = -6*1 = -6.

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What is the value of
(d)/(dx)(x^(-6)) at
x=1 ?

What is the value of $\frac{d}{d x}\left(x^{-6}\right)$ at $x=1$ ?

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Algebra 1

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Q. What is the value of

\frac{d}{d x}\left(x^{-6}\right)

x=1

Apply Power Rule: We need to find the derivative of the function $f(x) = x^{-6}$ with respect to $x$ . To do this, we will 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 our function, we get $f'(x) = (-6)\cdot x^{(-6-1)} = -6\cdot x^{-7}$ .
Substitute $x=1$ : Now we need to evaluate the derivative at $x=1$ . So we substitute $x$ with $1$ in the derivative we found: $f'(1) = -6\cdot1^{-7}$ .
Evaluate $f'(1)$ : Since any non-zero number to the power of any real number is still that number, $1^{(-7)}$ is simply $1$ . Therefore, $f'(1) = -6 \times 1 = -6$ .