derivative of (x^2+1e^{x-1})

Lösung

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

2 x e^{x - 1} + e^{x - 1} (x^{2} + 1)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} + 1, g = e^{x - 1}

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

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

\frac{d}{d x} (e^{x - 1}) = e^{x - 1}

= 2 x e^{x - 1} + e^{x - 1} (x^{2} + 1)

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 7, y^{^{'}} (0) = - 3

x \frac{d y}{d x} + (3 x + 1) y = e^{- 3 x}

\frac{d}{d x} (3 2 x - 5)

\frac{d}{d x} (\frac{1}{1 + 4 x ^{2}} - arctan (2 x))

l a pl a ce t r an s f or m e^{- t} sin^{2} (t)