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Beliebt Rechnen >

derivative of x^3arccos(x)

Lösung

\frac{d}{d x} (x^{3} arccos (x))

Lösung

3 x^{2} arccos (x) - \frac{x ^{3}}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{3} arccos (x))

Wende die Produktregel an:

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

f = x^{3}, g = arccos (x)

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

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

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

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

Vereinfache

3 x^{2} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{3} : 3 x^{2} arccos (x) - \frac{x ^{3}}{1 - x ^{2}}

= 3 x^{2} arccos (x) - \frac{x ^{3}}{1 - x ^{2}}

Graph

Beliebte Beispiele

derivative of 1/4 x^4-x^3

integral of x*e^{-x/4}

integral of (6+t+t^2)/(sqrt(t))

(\partial)/(\partial x)((2x)/(x^2+y^2))

fläche x^6,x^3