derivative of (sqrt(25-x^2)/(32x))

Lösung

\frac{d}{d x} (\frac{25 - x ^{2}}{32 x})

- \frac{25}{32 x ^{2} 25 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{25 - x ^{2}}{32 x})

Entferne die Konstante:

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

= \frac{1}{32} \frac{d}{d x} (\frac{25 - 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} ( 25 - x ^{2} ) x - \frac{d x}{d x} 25 - x ^{2}}{x ^{2}}

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

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

= \frac{1}{32} \cdot \frac{( - \frac{x}{25 - x ^{2}} ) x - 1 \cdot 25 - x ^{2}}{x ^{2}}

Vereinfache

\frac{1}{32} \cdot \frac{( - \frac{x}{25 - x ^{2}} ) x - 1 \cdot 25 - x ^{2}}{x ^{2}} : - \frac{25}{32 x ^{2} 25 - x ^{2}}

= - \frac{25}{32 x ^{2} 25 - x ^{2}}

\int_{- 1}^{1} x^{2} e^{x^{3} + 1} d x

\frac{d}{d x} (4 x^{5} - \frac{3}{x ^{2}})

\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

d er i v a t i v e f (x) = x^{3} - 15 x

\frac{d}{d x} (3 cos (5 x))