derivative ln(xsqrt(x^2+7))

Lösung

ableitung von

ln (x x^{2} + 7)

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

= \frac{1}{x x ^{2} + 7} \cdot \frac{2 x ^{2} + 7}{x ^{2} + 7}

Vereinfache

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

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

\int \frac{( cos ( x ) )}{sin ( x )} d x

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

\frac{d}{d x} (\frac{x + 1}{x - 1})

x \to 0 + lim (1 + \frac{1}{x})

l a pl a ce t r an s f or m 5 e^{- 2 (t - 1)}