Question

Differentiate e3x sin x with respect to x​

Answer 1

Step-by-step explanation:

$y = {e}^{3x} \times \sin(x) \\ \frac{dy}{dx} = \frac{d}{dx} ( {e}^{3x} \times \sin(x) ) \\ = {e}^{3x} \frac{d}{dx} \sin(x) + \sin(x) \frac{d}{dx} {e}^{3x} \\ = ({e}^{3x} \times \cos(x)) + (\sin(x) \times {e}^{3x} \times \frac{d}{dx} 3x) \\ = ( {e}^{3x} \times \cos(x) ) + ( \sin(x) \times {e}^{3x} \times 3 \frac{d}{dx} x) \\ = ( {e}^{3x} \times \cos(x) ) + ( \sin(x) \times {e}^{3x} \times 3 \times 1) \\ = ( {e}^{3x} \times \cos(x) ) + ( \sin(x) \times {e}^{3x} \times 3 ) \\ = {e}^{3x} ( \cos(x) + 3 \sin(x) )$