derivative of (sqrt(9-x^2)/(8x))

Lösung

\frac{d}{d x} (\frac{9 - x ^{2}}{8 x})

- \frac{9}{8 x ^{2} 9 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 - x ^{2}}{8 x})

Entferne die Konstante:

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

= \frac{1}{8} \frac{d}{d x} (\frac{9 - x ^{2}}{x})

Wende die Quotientenregel an:

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

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( 9 - x ^{2} ) x - \frac{d x}{d x} 9 - x ^{2}}{x ^{2}}

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

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

= \frac{1}{8} \cdot \frac{( - \frac{x}{9 - x ^{2}} ) x - 1 \cdot 9 - x ^{2}}{x ^{2}}

Vereinfache

\frac{1}{8} \cdot \frac{( - \frac{x}{9 - x ^{2}} ) x - 1 \cdot 9 - x ^{2}}{x ^{2}} : - \frac{9}{8 x ^{2} 9 - x ^{2}}

= - \frac{9}{8 x ^{2} 9 - x ^{2}}

n = 1 \sum \infty \frac{( x ^{n} )}{7 n}

d er i v a t i v e - 2 x

\int t^{2} - 2 cos (t) d t

\int (14 x + 6 x) d x

y^{^{'}} + y = y x e^{x + 2}