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 e^{5 x + e^{5 x}} d x

in v erse l a pl a ce \frac{s}{2 s ^{2} + 4 s + 3}

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

\int x^{3} - 2 x^{- 2} + 6 x d x

t a y l or 9 + x^{2}