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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int sin (\frac{1}{7}) x d x

h \to 0 lim \frac{( ( h - 5 ) ^{2} - 25 )}{( h )}

\frac{d}{d y} (2 x y^{3})

\int - \frac{1}{s} e^{- s t} d t

\int x (4 x + 5)^{8} d x