What is the derivative of 6/(sqrt(x)-8/x) ?

The derivative of 6/(sqrt(x)-8/x) is (-3x^2+8x^{3/2})/(x^{7/2)}

What is the first derivative of 6/(sqrt(x)-8/x) ?

The first derivative of 6/(sqrt(x)-8/x) is (-3x^2+8x^{3/2})/(x^{7/2)}

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\frac{d}{d x} (\frac{6}{x} - \frac{8}{x})

\frac{- 3 x ^{2} + 8 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{6}{x} - \frac{8}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{6}{x}) - \frac{d}{d x} (\frac{8}{x})

\frac{d}{d x} (\frac{6}{x}) = - \frac{3}{x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{8}{x}) = - \frac{8}{x ^{2}}

= - \frac{3}{x ^{\frac{3}{2}}} - (- \frac{8}{x ^{2}})

Simplify

- \frac{3}{x ^{\frac{3}{2}}} - (- \frac{8}{x ^{2}}) : \frac{- 3 x ^{2} + 8 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

= \frac{- 3 x ^{2} + 8 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

a^{x}

\frac{d}{d x} (- cos (4 x))

\frac{\partial}{\partial x} (ln (x^{2} + x))

\frac{\partial}{\partial x} (4 x - 4 - y^{2})

\frac{85 t}{99 t - 85}

What is the derivative of 6/(sqrt(x)-8/x) ?
The derivative of 6/(sqrt(x)-8/x) is (-3x^2+8x^{3/2})/(x^{7/2)}
What is the first derivative of 6/(sqrt(x)-8/x) ?
The first derivative of 6/(sqrt(x)-8/x) is (-3x^2+8x^{3/2})/(x^{7/2)}