derivative (sqrt(9-x^2))/(32x)

Lösung

ableitung von

\frac{9 - x ^{2}}{32 x}

- \frac{9}{32 x ^{2} 9 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 - x ^{2}}{32 x})

Entferne die Konstante:

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

= \frac{1}{32} \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}{32} \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}{32} \cdot \frac{( - \frac{x}{9 - x ^{2}} ) x - 1 \cdot 9 - x ^{2}}{x ^{2}}

Vereinfache

\frac{1}{32} \cdot \frac{( - \frac{x}{9 - x ^{2}} ) x - 1 \cdot 9 - x ^{2}}{x ^{2}} : - \frac{9}{32 x ^{2} 9 - x ^{2}}

= - \frac{9}{32 x ^{2} 9 - x ^{2}}

d er i v a t i v e f (x) = 3 x^{3} (x^{2} - 2)

d er i v a t i v e f (x) = (3 x^{2} - 2) (5 x + 5)

\int \frac{1}{1 - cos ^{2} ( x )} d x

d er i v a t i v e 7 t + 6 t^{7}

a re a y = 5 x - x^{2}, y = - x