Let f(x)=(1)/(x^(7)). f^(')(x)=

Identify Function: Identify the function to differentiate. We are given the function f(x) = 1/x^7, which we need to differentiate with respect to x.Apply Power Rule: Apply the power rule for differentiation. 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 the function as f(x) = x^(-7) to apply the power rule.Differentiate Using Rule: Differentiate using the power rule. Taking the derivative of f(x) = x^(-7) with respect to x, we get f'(x) = -7*x^(-7-1) = -7*x^(-8).Simplify Expression: Simplify the expression. The derivative f'(x) = -7*x^(-8) can be rewritten as f'(x) = -7/(x^8) for clarity.

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Let $f(x)=\frac{1}{x^{7}}$ . $\newline$ $f^{\prime}(x)=$

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Algebra 1

Multiplication with rational exponents

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Q. Let

f(x)=\frac{1}{x^{7}}

\newline

f^{\prime}(x)=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = \frac{1}{x^7}$ , which we need to differentiate with respect to $x$ .
Apply Power Rule: Apply the power rule for differentiation. 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 the function as $f(x) = x^{-7}$ to apply the power rule.
Differentiate Using Rule: Differentiate using the power rule. $\newline$ Taking the derivative of $f(x) = x^{-7}$ with respect to $x$ , we get $f'(x) = -7\cdot x^{-7-1} = -7\cdot x^{-8}$ .
Simplify Expression: Simplify the expression. $\newline$ The derivative $f'(x) = -7x^{-8}$ can be rewritten as $f'(x) = -\frac{7}{x^8}$ for clarity.