What is the derivative of (sqrt(s)-6)/(sqrt(s)+2) ?

The derivative of (sqrt(s)-6)/(sqrt(s)+2) is 4/(sqrt(s)(\sqrt{s)+2)^2}

What is the first derivative of (sqrt(s)-6)/(sqrt(s)+2) ?

The first derivative of (sqrt(s)-6)/(sqrt(s)+2) is 4/(sqrt(s)(\sqrt{s)+2)^2}

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derivative of

\frac{s - 6}{s + 2}

\frac{4}{s ( s + 2 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{s - 6}{s + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d s} ( s - 6 ) ( s + 2 ) - \frac{d}{d s} ( s + 2 ) ( s - 6 )}{( s + 2 ) ^{2}}

\frac{d}{d s} (s - 6) = \frac{1}{2 s}

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

= \frac{\frac{1}{2 s} ( s + 2 ) - \frac{1}{2 s} ( s - 6 )}{( s + 2 ) ^{2}}

Simplify

\frac{\frac{1}{2 s} ( s + 2 ) - \frac{1}{2 s} ( s - 6 )}{( s + 2 ) ^{2}} : \frac{4}{s ( s + 2 ) ^{2}}

= \frac{4}{s ( s + 2 ) ^{2}}

\int_{0}^{\frac{π}{3}} 81 sin^{2} (x) d x

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

\frac{d}{d x} (e^{- \frac{x}{2}} cos (\frac{3}{2} x))

\frac{d}{d x} (- \frac{3}{2} x^{4} cos (x))

x^{2}, x

What is the derivative of (sqrt(s)-6)/(sqrt(s)+2) ?
The derivative of (sqrt(s)-6)/(sqrt(s)+2) is 4/(sqrt(s)(\sqrt{s)+2)^2}
What is the first derivative of (sqrt(s)-6)/(sqrt(s)+2) ?
The first derivative of (sqrt(s)-6)/(sqrt(s)+2) is 4/(sqrt(s)(\sqrt{s)+2)^2}