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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (y^{2} \cdot x^{4} \cdot e^{x} + 2)

\frac{d}{d x} (\frac{e ^{7 x} + e ^{- 7 x}}{x})

\int_{0}^{1} - x^{2} d x

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

l a pl a ce t r an s f or m 2 e^{- 3 t}