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Popular >

derivative of x^{-2/4}+x^{2/4}

Solution

derivative of

x^{- \frac{2}{4}} + x^{\frac{2}{4}}

Solution

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

Solution steps

\frac{d}{d x} (x^{- \frac{2}{4}} + x^{\frac{2}{4}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{- \frac{2}{4}}) + \frac{d}{d x} (x^{\frac{2}{4}})

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

\frac{d}{d x} (x^{\frac{2}{4}}) = \frac{1}{2 x ^{\frac{1}{2}}}

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

Popular Examples

integral from 0 to infinity of 3e^{-3x}

\int_{0}^{\infty} 3 e^{- 3 x} d x

derivative of 9/(8\sqrt[4]{x^3})

integral from 0 to 1 of 1/((x-1)^{2/3)}

\int_{0}^{1} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

derivative of (8x^{1/3})

\frac{d}{d x} ((8 x)^{\frac{1}{3}})

integral of-cos(t)sin^2(t)

\int - cos (t) sin^{2} (t) d t

Frequently Asked Questions (FAQ)

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