ddx(x.ex)= - Infinity Learn

A
$e^{x} (x + 1)$
B
$e^{x}$
C
$e^{x} (x + 2)$
D
$e^{x} (x + 3)$

Solution:

$\begin{array}{l} H e r e u = x, v = e^{x} \\ \frac{d}{d x} (x . e^{x}) = x . \frac{d}{d x} (e^{x}) + e^{x} \frac{d}{d x} (x) = x . e^{x} + e^{x} (1) (∵ \frac{d}{d x} (u v) = u . \frac{d}{d x} (v) + v \frac{d}{d x} (u)) \\ \frac{d}{d x} (x . e^{x}) = e^{x} (x + 1) \end{array}$

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

Solution:

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