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Beliebt Rechnen >

derivative (sqrt(s)-5)/(sqrt(s)+1)

Lösung

ableitung von

\frac{s - 5}{s + 1}

Lösung

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

Schritte zur Lösung

\frac{d}{d s} (\frac{s - 5}{s + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d s} ( s - 5 ) ( s + 1 ) - \frac{d}{d s} ( s + 1 ) ( s - 5 )}{( s + 1 ) ^{2}}

\frac{d}{d s} (s - 5) = \frac{1}{2 s}

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of t^2sin(5t)

\int t^{2} sin (5 t) d t

d/(dn)((1+i)^n+(1-i)^n)

\frac{d}{d n} ((1 + i)^{n} + (1 - i)^{n})

derivative of 4/x-1/(x^3)

\frac{d}{d x} (\frac{4}{x} - \frac{1}{x ^{3}})

integral from 1 to 3 of f(2x)

\int_{1}^{3} f (2 x) d x

limit as t approaches 0 of ln(t+1)

t \to 0 lim (ln (t + 1))