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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{7 x ^{2} + 3}{x ( x ^{2} + 3 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x (x^{2} + 3)^{3}) = (x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

= \frac{1}{x ( x ^{2} + 3 ) ^{3}} ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2})

Vereinfache

\frac{1}{x ( x ^{2} + 3 ) ^{3}} ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}) : \frac{7 x ^{2} + 3}{x ( x ^{2} + 3 )}

= \frac{7 x ^{2} + 3}{x ( x ^{2} + 3 )}

Graph

Beliebte Beispiele

derivative of (-9x^2+4^2)

\frac{d}{d x} ((- 9 x^{2} + 4)^{2})

fläche y=2x-x^2,y=0

a re a y = 2 x - x^{2}, y = 0

derivative cos(pix)(pi)

d er i v a t i v e cos (π x) (π)

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d er i v a t i v e f (x) = 4 π r^{2}

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\int_{0}^{1} x^{4} e^{2 x} d x