What is the derivative of (s^{(-1)/2}+7s)(1-s^{-1}) ?

The derivative of (s^{(-1)/2}+7s)(1-s^{-1}) is (-1/(2s^{3/2)}+7)(1-1/s)+(1+7s^{3/2})/(s^{5/2)}

What is the first derivative of (s^{(-1)/2}+7s)(1-s^{-1}) ?

The first derivative of (s^{(-1)/2}+7s)(1-s^{-1}) is (-1/(2s^{3/2)}+7)(1-1/s)+(1+7s^{3/2})/(s^{5/2)}

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derivative of

(s^{\frac{- 1}{2}} + 7 s) (1 - s^{- 1})

(- \frac{1}{2 s ^{\frac{3}{2}}} + 7) (1 - \frac{1}{s}) + \frac{1 + 7 s ^{\frac{3}{2}}}{s ^{\frac{5}{2}}}

Solution steps

\frac{d}{d s} ((s^{\frac{- 1}{2}} + 7 s) (1 - s^{- 1}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = s^{\frac{- 1}{2}} + 7 s, g = 1 - s^{- 1}

= \frac{d}{d s} (s^{\frac{- 1}{2}} + 7 s) (1 - s^{- 1}) + \frac{d}{d s} (1 - s^{- 1}) (s^{\frac{- 1}{2}} + 7 s)

\frac{d}{d s} (s^{\frac{- 1}{2}} + 7 s) = - \frac{1}{2 s ^{\frac{3}{2}}} + 7

\frac{d}{d s} (1 - s^{- 1}) = \frac{1}{s ^{2}}

= (- \frac{1}{2 s ^{\frac{3}{2}}} + 7) (1 - s^{- 1}) + \frac{1}{s ^{2}} (s^{\frac{- 1}{2}} + 7 s)

Simplify

(- \frac{1}{2 s ^{\frac{3}{2}}} + 7) (1 - s^{- 1}) + \frac{1}{s ^{2}} (s^{\frac{- 1}{2}} + 7 s) : (- \frac{1}{2 s ^{\frac{3}{2}}} + 7) (1 - \frac{1}{s}) + \frac{1 + 7 s ^{\frac{3}{2}}}{s ^{\frac{5}{2}}}

= (- \frac{1}{2 s ^{\frac{3}{2}}} + 7) (1 - \frac{1}{s}) + \frac{1 + 7 s ^{\frac{3}{2}}}{s ^{\frac{5}{2}}}

What is the derivative of (s^{(-1)/2}+7s)(1-s^{-1}) ?
The derivative of (s^{(-1)/2}+7s)(1-s^{-1}) is (-1/(2s^{3/2)}+7)(1-1/s)+(1+7s^{3/2})/(s^{5/2)}
What is the first derivative of (s^{(-1)/2}+7s)(1-s^{-1}) ?
The first derivative of (s^{(-1)/2}+7s)(1-s^{-1}) is (-1/(2s^{3/2)}+7)(1-1/s)+(1+7s^{3/2})/(s^{5/2)}