derivative of e^x(12x^2-24x+24)

Lösung

\frac{d}{d x} (e^{x} (12 x^{2} - 24 x + 24))

12 e^{x} x^{2}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (12 x^{2} - 24 x + 24))

Wende die Produktregel an:

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

f = e^{x}, g = 12 x^{2} - 24 x + 24

= \frac{d}{d x} (e^{x}) (12 x^{2} - 24 x + 24) + \frac{d}{d x} (12 x^{2} - 24 x + 24) e^{x}

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

\frac{d}{d x} (12 x^{2} - 24 x + 24) = 24 x - 24

= e^{x} (12 x^{2} - 24 x + 24) + (24 x - 24) e^{x}

Vereinfache

e^{x} (12 x^{2} - 24 x + 24) + (24 x - 24) e^{x} : 12 e^{x} x^{2}

= 12 e^{x} x^{2}

\frac{d}{d x} (e^{x t a n (x)})

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

a re a y^{2} = x - 1, 1, 3

\frac{d}{d x} (\frac{3 x + 1}{3 - 4 x})

\int 64 x^{3} (4 x^{2} - 1) d x