derivative of x^2arctan(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

\frac{1}{x ^{2} + 1} x^{2} = \frac{x ^{2}}{x ^{2} + 1}

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

\frac{2 d y}{d x} + 5 y = 4

x \to 0 lim (\frac{1}{3})

4 x y^{^{'}} - (1 + x) y = 2 x y^{2}

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

f a c t or t^{3} - 6 t^{2} + 9 t