derivative ln(x+sqrt(x^2-3))

Lösung

ableitung von

ln (x + x^{2} - 3)

\frac{1}{x ^{2} - 3}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1}{x ^{2} - 3}

\int_{0}^{1} 2 π (2 - y) (8 y^{2}) d y

\frac{\partial}{\partial x} (8 x^{6} y^{7} - 7 x^{5} y^{6})

\int 6 csc^{2} (x) d x

d er i v a t i v e \frac{1}{3} x^{3}

a re a y = - x^{2} + 3 x + 1, y = - x + 1