What is the derivative of (sqrt(s)-1)/(sqrt(s)+7) ?

The derivative of (sqrt(s)-1)/(sqrt(s)+7) is 4/(sqrt(s)(\sqrt{s)+7)^2}

What is the first derivative of (sqrt(s)-1)/(sqrt(s)+7) ?

The first derivative of (sqrt(s)-1)/(sqrt(s)+7) is 4/(sqrt(s)(\sqrt{s)+7)^2}

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derivative of

\frac{s - 1}{s + 7}

\frac{4}{s ( s + 7 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{\frac{1}{2 s} ( s + 7 ) - \frac{1}{2 s} ( s - 1 )}{( s + 7 ) ^{2}} : \frac{4}{s ( s + 7 ) ^{2}}

= \frac{4}{s ( s + 7 ) ^{2}}

\int ln (1 + t) d t

\int e^{- \frac{x}{100}} d x

\int 15 x^{2} e^{5 x^{3} - 6} d x

s \to 0 lim (\frac{- \frac{1}{s}}{1 + ( 3 + \frac{13}{s} ) ( \frac{7}{x s + 1} )})

x \to 1 + lim (\frac{3}{∣ x - 1 ∣})

What is the derivative of (sqrt(s)-1)/(sqrt(s)+7) ?
The derivative of (sqrt(s)-1)/(sqrt(s)+7) is 4/(sqrt(s)(\sqrt{s)+7)^2}
What is the first derivative of (sqrt(s)-1)/(sqrt(s)+7) ?
The first derivative of (sqrt(s)-1)/(sqrt(s)+7) is 4/(sqrt(s)(\sqrt{s)+7)^2}