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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

a (c x + d) - c (a x + b) : - b c + a d

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

\int \frac{7}{3 + 7 x ^{2}} d x

\frac{d}{d x} (ln (tan (x)))

\frac{d y}{d x} = 3 x + y

t an g e n t 9 x - 9 x

\frac{d}{d x} (ln (\frac{a ^{x}}{1 + a ^{x}}))