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Popular >

derivative of x^{2/3}-x^{1/3}

Solution

derivative of

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

Solution

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

Solution steps

\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{2}{3}}) - \frac{d}{d x} (x^{\frac{1}{3}})

\frac{d}{d x} (x^{\frac{2}{3}}) = \frac{2}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (x^{\frac{1}{3}}) = \frac{1}{3 x ^{\frac{2}{3}}}

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

Popular Examples

integral of 7sin(2)(x)cos(3)(x)

\int 7 sin (2) (x) cos (3) (x) d x

derivative of (x^2(x-1)/((x+1)^2))

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

(d^2)/(dx^2)(7/(8t^6))

\frac{d ^{2}}{d x ^{2}} (\frac{7}{8 t ^{6}})

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x \to 3 + lim (\frac{x ^{2} - 9}{x - 3})

derivative of (sqrt(x))/(5+x)derivative of

\frac{x}{5 + x}

Frequently Asked Questions (FAQ)

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