ddx[ex.sinx.ax]= - Infinity Learn

A
$e^{x} a^{x} [\sin x . \log a - \cos x + \sin x]$
B
$e^{x} a^{x} [\sin x . \log a - \cos x - \sin x]$
C
$e^{x} a^{x} [\sin x . \log a + \cos x - \sin x]$
D
$e^{x} a^{x} [\sin x . \log a + \cos x + \sin x]$

Solution:

$\begin{array}{l} H e r e u = e^{x}, v = \sin x, w = a^{x} \\ B y using \frac{d}{d x} [u v w] = u v \frac{d}{d x} (w) + v w \frac{d}{d x} (u) + u w \frac{d}{d x} (v) \\ \frac{d}{d x} [e^{x} . \sin x . a^{x}] = e^{x} \sin x \frac{d}{d x} (a^{x}) + e^{x} . a^{x} \frac{d}{d x} (\sin x) + a^{x} \sin x \frac{d}{d x} (e^{x}) \\ = e^{x} \sin x (a^{x} . \log a) + e^{x} a^{x} \cos x + a^{x} \sin x (e^{x}) \\ = e^{x} a^{x} [\sin x . \log a + \cos x + \sin x] \end{array}$

$\frac{d}{d x} [e^{x} . \sin x . a^{x}] =$

Solution:

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