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Beliebt Rechnen >

derivative of ln(sqrt(x^2+3))

Lösung

\frac{d}{d x} (ln (x^{2} + 3))

Lösung

\frac{x}{x ^{2} + 3}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} + 3))

Wende die Kettenregel an:

\frac{1}{x ^{2} + 3} \frac{d}{d x} (x^{2} + 3)

= \frac{1}{x ^{2} + 3} \frac{d}{d x} (x^{2} + 3)

\frac{d}{d x} (x^{2} + 3) = \frac{x}{x ^{2} + 3}

= \frac{1}{x ^{2} + 3} \cdot \frac{x}{x ^{2} + 3}

Vereinfache

\frac{1}{x ^{2} + 3} \cdot \frac{x}{x ^{2} + 3} : \frac{x}{x ^{2} + 3}

= \frac{x}{x ^{2} + 3}

Graph

Beliebte Beispiele

derivative of 3^{(x^4+1^3})

\frac{d}{d x} (3^{(x^{4} + 1)^{3}})

integral of (3x^2-5x+1)/((x-4))

\int \frac{3 x ^{2} - 5 x + 1}{( x - 4 )} d x

maclaurin e^{x^5}

ma c l a u r in e^{x^{5}}

derivative f(x)=x^3-3x^2

d er i v a t i v e f (x) = x^{3} - 3 x^{2}

(d^2)/(dx^2)(sqrt(x)+\sqrt[3]{x})

\frac{d ^{2}}{d x ^{2}} (x + 3 x)