derivative of (ax+b/(cx+k))

Lösung

\frac{d}{d x} (\frac{a x + b}{c x + k})

\frac{- b c + ak}{( c x + k ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{a x + b}{c x + k})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( a x + b ) ( c x + k ) - \frac{d}{d x} ( c x + k ) ( a x + b )}{( c x + k ) ^{2}}

\frac{d}{d x} (a x + b) = a

\frac{d}{d x} (c x + k) = c

= \frac{a ( c x + k ) - c ( a x + b )}{( c x + k ) ^{2}}

Multipliziere aus

a (c x + k) - c (a x + b) : - b c + ak

= \frac{- b c + ak}{( c x + k ) ^{2}}

in v erse l a pl a ce ln (s)

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

d er i v a t i v e f (x) = e^{3 x^{2}}

\frac{d}{d x} (3 2 x^{5})

\int - 7 x - 3 + \frac{2}{x - 1} d x