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Beliebt Rechnen >

derivative of ln(sqrt(x^2+5))

Lösung

\frac{d}{d x} (ln (x^{2} + 5))

Lösung

\frac{x}{x ^{2} + 5}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} + 5))

Wende die Kettenregel an:

\frac{1}{x ^{2} + 5} \frac{d}{d x} (x^{2} + 5)

= \frac{1}{x ^{2} + 5} \frac{d}{d x} (x^{2} + 5)

\frac{d}{d x} (x^{2} + 5) = \frac{x}{x ^{2} + 5}

= \frac{1}{x ^{2} + 5} \cdot \frac{x}{x ^{2} + 5}

Vereinfache

\frac{1}{x ^{2} + 5} \cdot \frac{x}{x ^{2} + 5} : \frac{x}{x ^{2} + 5}

= \frac{x}{x ^{2} + 5}

Graph

Beliebte Beispiele

integral of 4e^{4x}

\int 4 e^{4 x} d x

integral of x/(x^3+x^2+4x+4)

\int \frac{x}{x ^{3} + x ^{2} + 4 x + 4} d x

(dy)/(dx)=y(xy^2-1)

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

integral of (tan(x)+sec(x))^2

\int (tan (x) + sec (x))^{2} d x

integral of-csc(2x)cot(2x)

\int - csc (2 x) cot (2 x) d x