d/(dy)(2sqrt(1-y^2-(x/4)^2))

Lösung

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

- \frac{8 y}{16 - 16 y ^{2} - x ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 \cdot \frac{1}{2 1 - y ^{2} - ( \frac{x}{4} ) ^{2}} (- 2 y) : - \frac{8 y}{16 - 16 y ^{2} - x ^{2}}

= - \frac{8 y}{16 - 16 y ^{2} - x ^{2}}

d er i v a t i v e f (x) = 17.19 8^{2} - x^{2}

\frac{d}{d x} (e^{x e^{y}})

\frac{d}{d x} (- cot (2 x))

\frac{d}{d x} (cos (x^{2}))

\frac{d y}{d x} = \frac{6}{5} (1 - \frac{y}{8})