derivative (6x)/(sqrt(x^2+2))

Lösung

ableitung von

\frac{6 x}{x ^{2} + 2}

\frac{12}{( x ^{2} + 2 ) x ^{2} + 2}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x}{x ^{2} + 2})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (\frac{x}{x ^{2} + 2})

Wende die Quotientenregel an:

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

= 6 \cdot \frac{\frac{d x}{d x} x ^{2} + 2 - \frac{d}{d x} ( x ^{2} + 2 ) x}{( x ^{2} + 2 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 2) = \frac{x}{x ^{2} + 2}

= 6 \cdot \frac{1 \cdot x ^{2} + 2 - \frac{x}{x ^{2} + 2} x}{( x ^{2} + 2 ) ^{2}}

Vereinfache

6 \cdot \frac{1 \cdot x ^{2} + 2 - \frac{x}{x ^{2} + 2} x}{( x ^{2} + 2 ) ^{2}} : \frac{12}{( x ^{2} + 2 ) x ^{2} + 2}

= \frac{12}{( x ^{2} + 2 ) x ^{2} + 2}

\frac{d y}{d x} = \frac{1}{x 16 x ^{2} - 1}

d er i v a t i v e f (x) = (x^{2} - 4) (x + 1)

a re a 4 x, x^{2} - 12

t^{2} y^{^{''}} + 7 t y^{^{'}} + 5 y = 0

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