derivative of (x+1*e^{arctan(x)})

Lösung

\frac{d}{d x} ((x + 1) \cdot e^{a r c t a n (x)})

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

Schritte zur Lösung

\frac{d}{d x} ((x + 1) e^{a r c t a n (x)})

Wende die Produktregel an:

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

f = x + 1, g = e^{a r c t a n (x)}

= \frac{d}{d x} (x + 1) e^{a r c t a n (x)} + \frac{d}{d x} (e^{a r c t a n (x)}) (x + 1)

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

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

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

Vereinfache

1 \cdot e^{a r c t a n (x)} + \frac{e ^{a r c t a n (x)}}{x ^{2} + 1} (x + 1) : \frac{e ^{a r c t a n (x)} x ^{2} + e ^{a r c t a n (x)} x + 2 e ^{a r c t a n (x)}}{x ^{2} + 1}

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

\frac{d}{d x} (- e^{- x^{2}})

\frac{d y}{d t} = 3 y + y^{4}

\int 4 x + 5 d x

(\frac{3}{3})^{^{'}}

\frac{d}{d x} (cos (x) cos (2 x) cos (4 x) sin (x))