What is (\partial)/(\partial x)(4x^{-1/2}-6/x) ?

The answer to (\partial)/(\partial x)(4x^{-1/2}-6/x) is (-2x^2+6x^{3/2})/(x^{7/2)}

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(\partial)/(\partial x)(4x^{-1/2}-6/x)

\frac{\partial}{\partial x} (4 x^{- \frac{1}{2}} - \frac{6}{x})

\frac{- 2 x ^{2} + 6 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

Solution steps

\frac{\partial}{\partial x} (4 x^{- \frac{1}{2}} - \frac{6}{x})

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{- \frac{1}{2}}) - \frac{\partial}{\partial x} (\frac{6}{x})

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

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

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

Simplify

- \frac{2}{x ^{\frac{3}{2}}} - (- \frac{6}{x ^{2}}) : \frac{- 2 x ^{2} + 6 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

= \frac{- 2 x ^{2} + 6 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

\frac{\partial}{\partial x} (ln (9 + x^{2} + 3 y^{2}))

\frac{d}{d x} (\frac{6}{( x - 1 ) ^{4}})

\frac{d}{d x} (sin (x^{2} + 2))

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

\frac{\partial}{\partial x} (x^{2} + 8)

What is (\partial)/(\partial x)(4x^{-1/2}-6/x) ?
The answer to (\partial)/(\partial x)(4x^{-1/2}-6/x) is (-2x^2+6x^{3/2})/(x^{7/2)}