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Find the derivative of $f(x)$ . $\newline$ $f(x) = \frac{1}{x^3}$ $\newline$ Write your answer as a constant times a power of $x$ . $\newline$ $f'(x) =$ ______

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Q. Find the derivative of

f(x)

.

\newline

f(x) = \frac{1}{x^3}

\newline

Write your answer as a constant times a power of

x

.

\newline

f'(x) =

______

Rewrite function as single power: Rewrite the function as a single power of $x$ . The function $f(x) = \frac{1}{x^3}$ can be rewritten using negative exponents as $f(x) = x^{-3}$ .
Apply power rule for differentiation: Apply the power rule for differentiation, which states that the derivative of $x^n$ is $n \cdot x^{n-1}$ . So, we will differentiate $f(x) = x^{-3}$ .
Perform the differentiation: Perform the differentiation: $f'(x) = -3x^{(-3 - 1)}$ . This follows directly from the power rule.
Simplify the expression: Simplify the expression by combining the exponents: $-3 - 1$ becomes $-4$ . So, the derivative $f'(x)$ is $-3x^{-4}$ .

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\newline

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\newline

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\newline

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\newline

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\newline

1

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