derivative (sqrt(s)-1)/(sqrt(s)+7)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\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}}

Vereinfache

\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 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 ∣})

ma c l a u r in x^{3}