derivative of xe^{2x^2-4x}

Lösung

\frac{d}{d x} (x e^{2 x^{2} - 4 x})

e^{2 x^{2} - 4 x} + e^{2 x^{2} - 4 x} x (4 x - 4)

Schritte zur Lösung

\frac{d}{d x} (x e^{2 x^{2} - 4 x})

Wende die Produktregel an:

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

f = x, g = e^{2 x^{2} - 4 x}

= \frac{d x}{d x} e^{2 x^{2} - 4 x} + \frac{d}{d x} (e^{2 x^{2} - 4 x}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{2 x^{2} - 4 x}) = e^{2 x^{2} - 4 x} (4 x - 4)

= 1 \cdot e^{2 x^{2} - 4 x} + e^{2 x^{2} - 4 x} (4 x - 4) x

Vereinfache

= e^{2 x^{2} - 4 x} + e^{2 x^{2} - 4 x} x (4 x - 4)

t an g e n t y = x^{3} - 2 x + 2, (4, 58)

d er i v a t i v e - \frac{1}{( 1 - x ) ^{2}}

t a y l or \frac{2}{x}, 1

\frac{d y}{d x} = 4 x (x - 1)

\int_{0}^{1} (x 1 - x^{2}) d x