What is the derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) ?

The derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) is -1/(4x^{3/2)}-7/(64x^{15/8)}

What is the first derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) ?

The first derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) is -1/(4x^{3/2)}-7/(64x^{15/8)}

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\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}})

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{7}{64 x ^{\frac{15}{8}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}})

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}{8 x ^{\frac{7}{8}}})

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

\frac{d}{d x} (\frac{1}{8 x ^{\frac{7}{8}}}) = - \frac{7}{64 x ^{\frac{15}{8}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{7}{64 x ^{\frac{15}{8}}}

e^{- 2 t} (2 cos (3 t) - sin (3 t))

x \to \infty lim (\frac{5}{x})

\int_{1}^{4} \frac{x + 4}{2 x} d x

6 x (x^{2} + 1)^{2}

x^{^{'}}

What is the derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) ?
The derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) is -1/(4x^{3/2)}-7/(64x^{15/8)}
What is the first derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) ?
The first derivative of 1/(2sqrt(x)+1/(8x^{7/8)}) is -1/(4x^{3/2)}-7/(64x^{15/8)}