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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

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

\frac{d}{d x} (1) = 0

= \frac{2}{x} + 2 y \frac{d y}{d x} - 0

Vereinfache

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

\frac{d}{d x} ((\frac{( 3 x + 1 )}{x ^{2}})^{3})

x \to + 0 lim (x (x - [x]))

\frac{\partial}{\partial x} (- 2 y^{3} sin (2 x))

d x - x + y d y = 0

\int e^{17 x} d x