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Beliebt Rechnen >

derivative of ln(sqrt(x^2+7))

Lösung

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

Lösung

\frac{x}{x ^{2} + 7}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as x approaches pi/2 of sin(x)

x \to \frac{π}{2} lim (sin (x))

integral of 6/(x^2+10x+16)

\int \frac{6}{x ^{2} + 10 x + 16} d x

integral of 6sin^4(x)

\int 6 sin^{4} (x) d x

derivative y=ln((x^2-1)/(x^2+1))

d er i v a t i v e y = ln (\frac{x ^{2} - 1}{x ^{2} + 1})

derivative-10e^{-5x^2}x

d er i v a t i v e - 10 e^{- 5 x^{2}} x