derivative of x/(sqrt(x^2+81))

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

\frac{81}{( x ^{2} + 81 ) x ^{2} + 81}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} x ^{2} + 81 - \frac{d}{d x} ( x ^{2} + 81 ) x}{( x ^{2} + 81 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 81) = \frac{x}{x ^{2} + 81}

= \frac{1 \cdot x ^{2} + 81 - \frac{x}{x ^{2} + 81} x}{( x ^{2} + 81 ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} + 81 - \frac{x}{x ^{2} + 81} x}{( x ^{2} + 81 ) ^{2}} : \frac{81}{( x ^{2} + 81 ) x ^{2} + 81}

= \frac{81}{( x ^{2} + 81 ) x ^{2} + 81}

d er i v a t i v e f (x) = 3 x + \frac{8}{x ^{3}}

n = 0 \sum \infty n + (- 1)^{n}

d er i v a t i v e \frac{e ^{x} + e ^{- x}}{e ^{2 x}}

(2 x^{4})^{^{'}}

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