derivative of (3x^2-6x+6e^x)

Lösung

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{x})

3 e^{x} x^{2}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{x})

Wende die Produktregel an:

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

f = 3 x^{2} - 6 x + 6, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 6 x + 6) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 6 x + 6)

\frac{d}{d x} (3 x^{2} - 6 x + 6) = 6 x - 6

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

= (6 x - 6) e^{x} + e^{x} (3 x^{2} - 6 x + 6)

Vereinfache

(6 x - 6) e^{x} + e^{x} (3 x^{2} - 6 x + 6) : 3 e^{x} x^{2}

= 3 e^{x} x^{2}

\int_{0}^{h} \frac{1}{2 h x} d x

\int (x^{2} + 5) ln (x) d x

d er i v a t i v e \frac{3 x}{x}

\int \frac{- 16}{4 - x ^{2}} d x

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0