derivative f(x)=ln(x+sqrt(x^2-12))

Lösung

ableitung von

f (x) = ln (x + x^{2} - 12)

\frac{1}{x ^{2} - 12}

Schritte zur Lösung

\frac{d}{d x} (ln (x + x^{2} - 12))

Wende die Kettenregel an:

\frac{1}{x + x ^{2} - 12} \frac{d}{d x} (x + x^{2} - 12)

= \frac{1}{x + x ^{2} - 12} \frac{d}{d x} (x + x^{2} - 12)

\frac{d}{d x} (x + x^{2} - 12) = 1 + \frac{x}{x ^{2} - 12}

= \frac{1}{x + x ^{2} - 12} (1 + \frac{x}{x ^{2} - 12})

Vereinfache

\frac{1}{x + x ^{2} - 12} (1 + \frac{x}{x ^{2} - 12}) : \frac{1}{x ^{2} - 12}

= \frac{1}{x ^{2} - 12}

t an g e n t y = \frac{- 2 x}{( x ^{2} + 1 )}

x \to 0 lim (\frac{x}{0})

x \to - 2 lim (x^{2} + 3 x - 7)

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

f (x) = - e^{x} x + 3 e^{x}