derivative of (1+x^2arctan(x))

Lösung

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

2 x arctan (x) + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 1 + x^{2}, g = arctan (x)

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

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

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

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

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

= 2 x arctan (x) + 1

d er i v a t i v e x^{3} y - y^{2}

\int (tan (4 x) + sec (4 x))^{2} d x

\frac{\partial}{\partial x} (e^{3 x - y})

t an g e n t f (x) = 3 e^{1 - x^{2}}, (1, 3)

n = 0 \sum \infty - \frac{1}{5 ^{n}}