de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of sqrt(1+x^2+y^2)

Lösung

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

Lösung

\frac{x + y \frac{d y}{d x}}{1 + x ^{2} + y ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{x + y \frac{d y}{d x}}{1 + x ^{2} + y ^{2}}

Beliebte Beispiele

(dy)/(dx)=2y(1-y)

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

derivative (x^2+5x+6)/(x^2-4)

d er i v a t i v e \frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

derivative 2/((6x^2+5x+1)^2)

d er i v a t i v e \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}}

integral of 1/(aauu)

\int \frac{1}{aa uu} d u

derivative of 1/(sin(x^2))

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