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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

Simplify

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

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

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\frac{d y}{d x} = 4 x + \frac{9 x ^{2}}{( 3 x ^{3} + 1 ) ^{\frac{3}{2}}}

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\frac{d}{d x} (- 9 x^{2} + 4 x + 5)

\int cot^{4} (x) d x

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