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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{x ^{n}}{n !} d x

\frac{d y}{d t} - \frac{y}{2 t} = 3 t

x \to 0 lim (ln (x^{2}) - x^{- 2})

\frac{d}{d x} ((x^{3} - 9 x)^{- \frac{1}{3}})

\frac{d}{d x} (tan (cot (ln (x))) + sec (e^{x}))