What is the derivative of f(x)= 1/(x^6) ?

The derivative of f(x)= 1/(x^6) is -6/(x^7)

What is the first derivative of f(x)= 1/(x^6) ?

The first derivative of f(x)= 1/(x^6) is -6/(x^7)

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derivative of

f (x) = \frac{1}{x ^{6}}

- \frac{6}{x ^{7}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{6}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (x^{- 6})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 6 x^{- 6 - 1}

Simplify

- 6 x^{- 6 - 1} : - \frac{6}{x ^{7}}

= - \frac{6}{x ^{7}}

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What is the derivative of f(x)= 1/(x^6) ?
The derivative of f(x)= 1/(x^6) is -6/(x^7)
What is the first derivative of f(x)= 1/(x^6) ?
The first derivative of f(x)= 1/(x^6) is -6/(x^7)