What is the derivative of (s-sqrt(s))/(s^2) ?

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

What is the first derivative of (s-sqrt(s))/(s^2) ?

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

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derivative of

\frac{s - s}{s ^{2}}

\frac{- 2 s + 3}{2 s ^{\frac{5}{2}}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{- 2 s + 3}{2 s ^{\frac{5}{2}}}

y = 3 - x^{2}, y = - 1

\int_{a}^{b} \frac{1}{r ^{2}} d r

\frac{\partial}{\partial x} (e^{x} sin (2 y))

\int \frac{2 x + 4}{x} d x

x \to - 3 lim (\frac{( x + 3 )}{x - 3})

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