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Beliebt Rechnen >

derivative of ln(4x^2+1)

Lösung

\frac{d}{d x} (ln (4 x^{2} + 1))

Lösung

\frac{8 x}{4 x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (ln (4 x^{2} + 1))

Wende die Kettenregel an:

\frac{1}{4 x ^{2} + 1} \frac{d}{d x} (4 x^{2} + 1)

= \frac{1}{4 x ^{2} + 1} \frac{d}{d x} (4 x^{2} + 1)

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= \frac{1}{4 x ^{2} + 1} \cdot 8 x

Vereinfache

\frac{1}{4 x ^{2} + 1} \cdot 8 x : \frac{8 x}{4 x ^{2} + 1}

= \frac{8 x}{4 x ^{2} + 1}

Graph

Beliebte Beispiele

derivative of 1000(1-e^{-0.15x})

\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

derivative 3^xlog_{3}(x)

d er i v a t i v e 3^{x} lo g_{3} (x)

fläche 9-x^2,-8x

a re a 9 - x^{2}, - 8 x

derivative of x/(x+5)

\frac{d}{d x} (\frac{x}{x + 5})

(dy)/(dx)=x(4-y)

\frac{d y}{d x} = x (4 - y)