derivative of sqrt(x^2+2y^2-4)

Lösung

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

\frac{x + 2 y \frac{d y}{d x}}{x ^{2} + 2 y ^{2} - 4}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{x + 2 y \frac{d y}{d x}}{x ^{2} + 2 y ^{2} - 4}

(y - x) d x + 4 x d y = 0

\int \frac{1}{2 x - 1} d x

p a r i t y ln ∣ sin (x) ∣

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

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