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Beliebt Rechnen >

derivative of x^2arctan(x^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = arctan (x^{3})

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

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

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

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

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

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

Graph

Beliebte Beispiele

tangent x^3+4x^2+7x+1

t an g e n t x^{3} + 4 x^{2} + 7 x + 1

sum from n=2 to infinity of 6/(7^n)

n = 2 \sum \infty \frac{6}{7 ^{n}}

limit as x approaches-3 of (2x)/(x^2+4)

x \to - 3 lim (\frac{2 x}{x ^{2} + 4})

x y^{^{'}} - 2 y = 2 x^{2}

y^{''}+y^'-42y=0

y^{^{''}} + y^{^{'}} - 42 y = 0