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)}

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derivative of

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

- \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}}}

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)}