What is the derivative of f(x)=x^{-1/5}+x^{1/5} ?

The derivative of f(x)=x^{-1/5}+x^{1/5} is -1/(5x^{6/5)}+1/(5x^{4/5)}

What is the first derivative of f(x)=x^{-1/5}+x^{1/5} ?

The first derivative of f(x)=x^{-1/5}+x^{1/5} is -1/(5x^{6/5)}+1/(5x^{4/5)}

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derivative of

f (x) = x^{- \frac{1}{5}} + x^{\frac{1}{5}}

- \frac{1}{5 x ^{\frac{6}{5}}} + \frac{1}{5 x ^{\frac{4}{5}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x^{- \frac{1}{5}}) = - \frac{1}{5 x ^{\frac{6}{5}}}

\frac{d}{d x} (x^{\frac{1}{5}}) = \frac{1}{5 x ^{\frac{4}{5}}}

= - \frac{1}{5 x ^{\frac{6}{5}}} + \frac{1}{5 x ^{\frac{4}{5}}}

What is the derivative of f(x)=x^{-1/5}+x^{1/5} ?
The derivative of f(x)=x^{-1/5}+x^{1/5} is -1/(5x^{6/5)}+1/(5x^{4/5)}
What is the first derivative of f(x)=x^{-1/5}+x^{1/5} ?
The first derivative of f(x)=x^{-1/5}+x^{1/5} is -1/(5x^{6/5)}+1/(5x^{4/5)}