What is the derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) ?

The derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) is -1/(4x^{3/2)}-4/(25x^{9/5)}

What is the first derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) ?

The first derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) is -1/(4x^{3/2)}-4/(25x^{9/5)}

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\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{5 x ^{\frac{4}{5}}})

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{4}{25 x ^{\frac{9}{5}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{5 x ^{\frac{4}{5}}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{2 x}) + \frac{d}{d x} (\frac{1}{5 x ^{\frac{4}{5}}})

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

\frac{d}{d x} (\frac{1}{5 x ^{\frac{4}{5}}}) = - \frac{4}{25 x ^{\frac{9}{5}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{4}{25 x ^{\frac{9}{5}}}

What is the derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) ?
The derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) is -1/(4x^{3/2)}-4/(25x^{9/5)}
What is the first derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) ?
The first derivative of 1/(2sqrt(x)+1/(5x^{4/5)}) is -1/(4x^{3/2)}-4/(25x^{9/5)}