derivative of (x+2^{arctan(x)})

Lösung

\frac{d}{d x} ((x + 2)^{a r c t a n (x)})

(\frac{ln ( x + 2 )}{x ^{2} + 1} + \frac{arctan ( x )}{x + 2}) (x + 2)^{a r c t a n (x)}

Schritte zur Lösung

\frac{d}{d x} ((x + 2)^{a r c t a n (x)})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(x + 2)^{a r c t a n (x)} = e^{a r c t a n (x) l n (x + 2)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (x + 2)})

Wende die Kettenregel an:

e^{a r c t a n (x) l n (x + 2)} \frac{d}{d x} (arctan (x) ln (x + 2))

= e^{a r c t a n (x) l n (x + 2)} \frac{d}{d x} (arctan (x) ln (x + 2))

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

= e^{a r c t a n (x) l n (x + 2)} (\frac{ln ( x + 2 )}{x ^{2} + 1} + \frac{arctan ( x )}{x + 2})

e^{a r c t a n (x) l n (x + 2)} = (x + 2)^{a r c t a n (x)}

= (\frac{ln ( x + 2 )}{x ^{2} + 1} + \frac{arctan ( x )}{x + 2}) (x + 2)^{a r c t a n (x)}

\frac{\partial}{\partial y} (\frac{2 x + 3}{4 y + 1})

\int x e^{x} d x

y^{^{''}} - \frac{y ^{^{'}}}{x} = 3 x

d er i v a t i v e \frac{x ^{5}}{5}

y^{^{'}} + 2 y = x e^{- 2 x}