derivative of e^x(5x^2-2x+3)

Lösung

\frac{d}{d x} (e^{x} (5 x^{2} - 2 x + 3))

5 e^{x} x^{2} + 8 e^{x} x + e^{x}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (5 x^{2} - 2 x + 3))

Wende die Produktregel an:

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

f = e^{x}, g = 5 x^{2} - 2 x + 3

= \frac{d}{d x} (e^{x}) (5 x^{2} - 2 x + 3) + \frac{d}{d x} (5 x^{2} - 2 x + 3) e^{x}

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

\frac{d}{d x} (5 x^{2} - 2 x + 3) = 10 x - 2

= e^{x} (5 x^{2} - 2 x + 3) + (10 x - 2) e^{x}

Vereinfache

e^{x} (5 x^{2} - 2 x + 3) + (10 x - 2) e^{x} : 5 e^{x} x^{2} + 8 e^{x} x + e^{x}

= 5 e^{x} x^{2} + 8 e^{x} x + e^{x}

\frac{d y}{d x} = \frac{y sin ( x )}{1 - 2 y}

y^{^{'}} = e^{y - x}, y (0) = 0

\frac{d}{d x} (c x^{- 8})

d er i v a t i v e x^{2}

\frac{\partial}{\partial x} (e^{x y z^{6}})