derivative h(x)=ln(x+sqrt(x^2-7))

Lösung

ableitung von

h (x) = ln (x + x^{2} - 7)

\frac{1}{x ^{2} - 7}

Schritte zur Lösung

\frac{d}{d x} (ln (x + x^{2} - 7))

Wende die Kettenregel an:

\frac{1}{x + x ^{2} - 7} \frac{d}{d x} (x + x^{2} - 7)

= \frac{1}{x + x ^{2} - 7} \frac{d}{d x} (x + x^{2} - 7)

\frac{d}{d x} (x + x^{2} - 7) = 1 + \frac{x}{x ^{2} - 7}

= \frac{1}{x + x ^{2} - 7} (1 + \frac{x}{x ^{2} - 7})

Vereinfache

\frac{1}{x + x ^{2} - 7} (1 + \frac{x}{x ^{2} - 7}) : \frac{1}{x ^{2} - 7}

= \frac{1}{x ^{2} - 7}

in v erse l a pl a ce \frac{- 2 s + 1}{s ^{2} + 2 s - 8}

x \to 0 lim (\frac{x + 4}{x})

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 9 y^{3})

a re a x^{3}, - x, 1

x \to 0 lim (4 - ln (x))