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Beliebt Rechnen >

derivative of x^2arctan(ln(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

Graph

Beliebte Beispiele

derivative e^{x^2-9}

d er i v a t i v e e^{x^{2} - 9}

derivative 2x^4-x^3+6x^2

d er i v a t i v e 2 x^{4} - x^{3} + 6 x^{2}

derivative a(t)=t^3-12t

d er i v a t i v e a (t) = t^{3} - 12 t

integral of+x^2sqrt(a^2-x^2)

\int + x^{2} a^{2} - x^{2} d x

integral of (e^{9sqrt(t)})/(sqrt(t))

\int \frac{e ^{9 t}}{t} d t