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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

f (x) = \frac{6}{5 x + 3}

\int_{0}^{2 π} e^{i x} d x

\frac{2 x}{x + 1}, at x = 1

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

\int x^{6} e^{- 4 x} d x

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