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Beliebt Rechnen >

derivative of x^3ln(x^4+1)

Lösung

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

Lösung

3 x^{2} ln (x^{4} + 1) + \frac{4 x ^{6}}{x ^{4} + 1}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = ln (x^{4} + 1)

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

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

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

= 3 x^{2} ln (x^{4} + 1) + \frac{4 x ^{3}}{x ^{4} + 1} x^{3}

\frac{4 x ^{3}}{x ^{4} + 1} x^{3} = \frac{4 x ^{6}}{x ^{4} + 1}

= 3 x^{2} ln (x^{4} + 1) + \frac{4 x ^{6}}{x ^{4} + 1}

Graph

Beliebte Beispiele

integral from 2 to x^2 of cos(t^2+1)

\int_{2}^{x^{2}} cos (t^{2} + 1) d t

derivative y=xcos(x)

d er i v a t i v e y = x cos (x)

fläche x=63-7y^2,x=7y^2-63

a re a x = 63 - 7 y^{2}, x = 7 y^{2} - 63

derivative t^3-t

d er i v a t i v e t^{3} - t

derivative of sqrt(1-x^2)-xarccos(x)

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