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Popular >

derivative of sqrt(x)+x^{-1/3}

Solution

derivative of

x + x^{- \frac{1}{3}}

Solution

\frac{1}{2 x ^{\frac{1}{2}}} - \frac{1}{3 x ^{\frac{4}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x ^{\frac{1}{2}}}

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

= \frac{1}{2 x ^{\frac{1}{2}}} - \frac{1}{3 x ^{\frac{4}{3}}}

Popular Examples

(\partial)/(\partial x)(3x^2y-3x+3y^3)

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\int \frac{x ^{2}}{( x - 1 ) ( x - 2 )} d x

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\int \frac{x ^{3}}{( 1 - x ^{4} ) ^{7}} d x

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\int cos (x) - sin (x) + sec^{2} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)+x^{-1/3} ?
The derivative of sqrt(x)+x^{-1/3} is 1/(2x^{1/2)}-1/(3x^{4/3)}
What is the first derivative of sqrt(x)+x^{-1/3} ?
The first derivative of sqrt(x)+x^{-1/3} is 1/(2x^{1/2)}-1/(3x^{4/3)}