derivative of (2000x/(4x+75))

Lösung

\frac{d}{d x} (\frac{2000 x}{4 x + 75})

\frac{150000}{( 4 x + 75 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2000 x}{4 x + 75})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2000 \frac{d}{d x} (\frac{x}{4 x + 75})

Wende die Quotientenregel an:

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

= 2000 \cdot \frac{\frac{d x}{d x} ( 4 x + 75 ) - \frac{d}{d x} ( 4 x + 75 ) x}{( 4 x + 75 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (4 x + 75) = 4

= 2000 \cdot \frac{1 \cdot ( 4 x + 75 ) - 4 x}{( 4 x + 75 ) ^{2}}

Vereinfache

2000 \cdot \frac{1 \cdot ( 4 x + 75 ) - 4 x}{( 4 x + 75 ) ^{2}} : \frac{150000}{( 4 x + 75 ) ^{2}}

= \frac{150000}{( 4 x + 75 ) ^{2}}

f (x) = 6 x arcsin (x)

\int sin^{2} (\frac{5 x}{2}) d x

(2 x + 1) y^{^{'}} + 2 y = 4 x

\frac{d}{d x} (1 - sec^{2} (x))

\int \frac{1}{5 y} d y