derivative of e^x(6x^2-12x+12)

Lösung

\frac{d}{d x} (e^{x} (6 x^{2} - 12 x + 12))

6 e^{x} x^{2}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (6 x^{2} - 12 x + 12))

Wende die Produktregel an:

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

f = e^{x}, g = 6 x^{2} - 12 x + 12

= \frac{d}{d x} (e^{x}) (6 x^{2} - 12 x + 12) + \frac{d}{d x} (6 x^{2} - 12 x + 12) e^{x}

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

\frac{d}{d x} (6 x^{2} - 12 x + 12) = 12 x - 12

= e^{x} (6 x^{2} - 12 x + 12) + (12 x - 12) e^{x}

Vereinfache

e^{x} (6 x^{2} - 12 x + 12) + (12 x - 12) e^{x} : 6 e^{x} x^{2}

= 6 e^{x} x^{2}

\frac{d}{d y} (\frac{1}{y ^{2}})

x \to 2 lim (h (x))

\frac{d y}{d x} - 2 x y = - 3 x^{2} e^{x^{2}}

y \to 5 lim (\frac{25 - y ^{2}}{y ^{2} - 4 y - 5})

\int \frac{sin ( 2 t + 1 )}{cos ^{2} ( 2 t + 1 )} d t