derivative of (Ax+B/(Cx+d))

Lösung

\frac{d}{d x} (\frac{A x + B}{C x + d})

\frac{A d - BC}{( x C + d ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{A x + B}{C x + d})

Behandle

A, B, C, d

als Konstanten

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) : A d - BC

= \frac{A d - BC}{( x C + d ) ^{2}}

\int_{- 1}^{3} 3 x^{3} d x

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

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

x \to 3 lim (\frac{x ^{2} - 9}{x + 2})

l a pl a ce t r an s f or m 5 \cdot t^{3}