What is the derivative of (sqrt(s)-7)/(sqrt(s)+3) ?

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

What is the first derivative of (sqrt(s)-7)/(sqrt(s)+3) ?

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

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derivative of

\frac{s - 7}{s + 3}

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

Solution steps

\frac{d}{d s} (\frac{s - 7}{s + 3})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{( x ^{2} )}{x + 7}

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

\frac{\partial}{\partial x} (\frac{1}{( 1 + e ^{- x} )})

\frac{d}{d x} (lo g_{10} ((x - 3)^{2}))

\int \frac{4 x ^{2} + 1}{2 x + 5} d x

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