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

Lösung

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

12 e^{x} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} ((\frac{2}{3})^{x})

d er i v a t i v e f (x) = (4 x - 3) (x + 2)

d er i v a t i v e f (x) = x^{2} + 10

\int sec^{2} (x) tan^{10} (x) d x

t a y l or e^{(x + 1)}