derivative of x^2arccos(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = arccos (x)

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

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

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

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

Vereinfache

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

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

\int \frac{11 x + 17}{2 x ^{2} + 7 x - 4} d x

\int \frac{1}{3 x + 7 x} d x

\int \frac{8 - x ^{2}}{9} d x

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

\frac{d}{d x} (1 - 6 x^{2})