e x [ x n ⋅ sin x + x 3 ⋅ cos x + x n − 1 ⋅ sin x ]

ddx(xn⋅sinx⋅ex)= - Infinity Learn

A
$e^{x} [x^{n} \cdot \sin x + x^{3} \cdot \cos x - x^{n - 1} \cdot \sin x]$
B
$e^{x} [x^{n} \cdot \sin x + x^{3} \cdot \cos x + x^{n - 1} \cdot \sin x]$
C
$e^{x} [x^{n} \cdot \sin x - x^{3} \cdot \cos x + x^{n - 1} \cdot n \sin x]$
D
None of these

Solution:

$\frac{d}{d x} (x^{n} \cdot \sin x \cdot e^{x}) = x^{n} \cdot \sin x \cdot e^{x} + x^{n} \cdot e^{x} \cdot \cos x + \sin x \cdot e^{x} \cdot n . x^{n - 1}$

$= e^{x} [x^{n} \cdot \sin x + x^{n} \cdot \cos x + x^{n - 1} \cdot n \sin x]$

$\frac{d}{d x} (x^{n} \cdot \sin x \cdot e^{x}) =$

Solution:

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