derivative of e^x(x^2-2x+2)

Lösung

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

e^{x} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= e^{x} x^{2}

\int e^{s} sin (1 - s) d s

d er i v a t i v e 5 cos ((\frac{π}{4} x) + \frac{π}{4})

\frac{d}{d x} (3 x^{2} + y^{2} - 1)

\int_{0}^{1} (x - x^{4}) d x

a re a y = 3 x, y = 7 x^{2}