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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x + 6) = 1

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

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

Vereinfache

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

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

\frac{d}{d x} (3 x^{2} - 5 x + 6)

\frac{d y}{d x} = - 8 y

d er i v a t i v e f (x) = - 3 x + 1

\int \frac{3 x}{3 - x ^{2}} d x

d er i v a t i v e f (x) = - 5 x + 2