derivative 2\sqrt[4]{9-x^2}

Lösung

ableitung von

2 4 9 - x^{2}

- \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (2 4 9 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (4 9 - x^{2})

Wende die Kettenregel an:

\frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (9 - x^{2})

= \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (9 - x^{2})

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

= 2 \cdot \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x)

Vereinfache

2 \cdot \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x) : - \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

= - \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

\int \frac{cos ( θ )}{2 + sin ^{2} ( θ )} d θ

x \to 0 lim (\frac{4 x ^{2}}{x})

\frac{\partial}{\partial x} ((41 - x^{2} - y^{2})^{\frac{1}{2}})

\int_{0}^{1} x e^{- 4 x} d x

\frac{d}{d x} (3 e^{2 x} + 2 e^{2 x} x)