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Popular >

derivative of 5x-x^{-1/3}-1

Solution

\frac{d}{d x} (5 x - x^{- \frac{1}{3}} - 1)

Solution

\frac{1}{3 x ^{\frac{4}{3}}} + 5

Solution steps

\frac{d}{d x} (5 x - x^{- \frac{1}{3}} - 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (5 x) - \frac{d}{d x} (x^{- \frac{1}{3}}) - \frac{d}{d x} (1)

\frac{d}{d x} (5 x) = 5

\frac{d}{d x} (x^{- \frac{1}{3}}) = - \frac{1}{3 x ^{\frac{4}{3}}}

\frac{d}{d x} (1) = 0

= 5 - (- \frac{1}{3 x ^{\frac{4}{3}}}) - 0

Simplify

= \frac{1}{3 x ^{\frac{4}{3}}} + 5

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\int \frac{12}{x ^{2} - 9} d x

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Frequently Asked Questions (FAQ)

What is the derivative of 5x-x^{-1/3}-1 ?
The derivative of 5x-x^{-1/3}-1 is 1/(3x^{4/3)}+5
What is the first derivative of 5x-x^{-1/3}-1 ?
The first derivative of 5x-x^{-1/3}-1 is 1/(3x^{4/3)}+5