derivative (3sqrt(x))/(9x^2+4x-9)

Lösung

ableitung von

\frac{3 x}{9 x ^{2} + 4 x - 9}

\frac{3 ( - 27 x ^{2} - 4 x - 9 )}{2 x ( 9 x ^{2} + 4 x - 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x}{9 x ^{2} + 4 x - 9})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{x}{9 x ^{2} + 4 x - 9})

Wende die Quotientenregel an:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ) ( 9 x ^{2} + 4 x - 9 ) - \frac{d}{d x} ( 9 x ^{2} + 4 x - 9 ) x}{( 9 x ^{2} + 4 x - 9 ) ^{2}}

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

\frac{d}{d x} (9 x^{2} + 4 x - 9) = 18 x + 4

= 3 \cdot \frac{\frac{1}{2 x} ( 9 x ^{2} + 4 x - 9 ) - ( 18 x + 4 ) x}{( 9 x ^{2} + 4 x - 9 ) ^{2}}

Vereinfache

3 \cdot \frac{\frac{1}{2 x} ( 9 x ^{2} + 4 x - 9 ) - ( 18 x + 4 ) x}{( 9 x ^{2} + 4 x - 9 ) ^{2}} : \frac{3 ( - 27 x ^{2} - 4 x - 9 )}{2 x ( 9 x ^{2} + 4 x - 9 ) ^{2}}

= \frac{3 ( - 27 x ^{2} - 4 x - 9 )}{2 x ( 9 x ^{2} + 4 x - 9 ) ^{2}}

\int_{0}^{1} \frac{1}{4 x} d x

x \to 1 lim (\frac{[ x ]}{∣ x ∣})

x \to π lim (sin (6 x))

d er i v a t i v e x (3 x + 4)^{2}

\frac{\partial}{\partial x} (\frac{x}{x ^{3} + y ^{2}})