What is the derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 ?

The derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 is (-9-6x+6x^{9/2})/(2x^{5/2)}

What is the first derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 ?

The first derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 is (-9-6x+6x^{9/2})/(2x^{5/2)}

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derivative of

3 x^{- \frac{3}{2}} + 6 x^{- \frac{1}{2}} + x^{3} - 4

\frac{- 9 - 6 x + 6 x ^{\frac{9}{2}}}{2 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (3 x^{- \frac{3}{2}} + 6 x^{- \frac{1}{2}} + x^{3} - 4)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{- \frac{3}{2}}) + \frac{d}{d x} (6 x^{- \frac{1}{2}}) + \frac{d}{d x} (x^{3}) - \frac{d}{d x} (4)

\frac{d}{d x} (3 x^{- \frac{3}{2}}) = - \frac{9}{2 x ^{\frac{5}{2}}}

\frac{d}{d x} (6 x^{- \frac{1}{2}}) = - \frac{3}{x ^{\frac{3}{2}}}

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

\frac{d}{d x} (4) = 0

= - \frac{9}{2 x ^{\frac{5}{2}}} - \frac{3}{x ^{\frac{3}{2}}} + 3 x^{2} - 0

Simplify

- \frac{9}{2 x ^{\frac{5}{2}}} - \frac{3}{x ^{\frac{3}{2}}} + 3 x^{2} - 0 : \frac{- 9 - 6 x + 6 x ^{\frac{9}{2}}}{2 x ^{\frac{5}{2}}}

= \frac{- 9 - 6 x + 6 x ^{\frac{9}{2}}}{2 x ^{\frac{5}{2}}}

y = e^{3 x}

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

2 3 x

\int x 16 - x^{2} d x

\frac{d}{d s} (\frac{s ^{2} - 4 s + 20}{s ^{2} + 6 s + 8})

What is the derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 ?
The derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 is (-9-6x+6x^{9/2})/(2x^{5/2)}
What is the first derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 ?
The first derivative of 3x^{-3/2}+6x^{-1/2}+x^3-4 is (-9-6x+6x^{9/2})/(2x^{5/2)}