derivative of (Ax+B/(sqrt(4-x)))

Lösung

\frac{d}{d x} (\frac{A x + B}{4 - x})

\frac{8 A - A x + B}{2 ( 4 - x ) 4 - x}

Schritte zur Lösung

\frac{d}{d x} (\frac{A x + B}{4 - x})

Behandle

A, B

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

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

\frac{d}{d x} (4 - x) = - \frac{1}{2 4 - x}

= \frac{A 4 - x - ( - \frac{1}{2 4 - x} ) ( A x + B )}{( 4 - x ) ^{2}}

Vereinfache

\frac{A 4 - x - ( - \frac{1}{2 4 - x} ) ( A x + B )}{( 4 - x ) ^{2}} : \frac{8 A - A x + B}{2 ( 4 - x ) 4 - x}

= \frac{8 A - A x + B}{2 ( 4 - x ) 4 - x}

n = 1 \sum \infty \frac{3}{n !}

\frac{\partial}{\partial x} (4 x y^{2})

x \to 3 lim (9 - 9)

\frac{\partial}{\partial x} (\frac{x y}{x ^{2} - y ^{2}})

\frac{\partial}{\partial x} (\frac{a y x ^{2} z}{2})