Find dy/dx if y=e^2x sin2x ?

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Find dy/dx if y=e^2x sin2x ?

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Answer 1 · 2018-06-25T15:17:13

$\frac{d y}{d x} = e^{2} (sin (2 x) + 2 x cos (2 x))$ $dy/dx=e^2(sin(2x)+2xcos(2x))$

Explanation:

I'm assuming the function is $y = e^{2} x sin (2 x)$ $y=e^2xsin(2x)$ .
$\frac{d y}{d x} = \frac{d}{d x} (e^{2} x sin (2 x)) = e^{2} \frac{d}{d x} (x sin (2 x))$ $dy/dx=d/dx(e^2xsin(2x))=e^2d/dx(xsin(2x))$
To differentiate $x sin (2 x)$ $xsin(2x)$ , we will use the product rule:
$y=f(x)g(x)iffdy/dx=f'(x)g(x)+g'(x)f(x)$
Therefore, $d/dx(xsin(2x))=sin(2x)+2xcos(2x)$
Finally, we get $dy/dx=e^2(sin(2x)+2xcos(2x))$ .

*If the original function was supposed to be $y=e^(2x)sin2x$ , $dy/dx=2e^(2x)sin(2x)+2e^(2x)cos(2x)$ by the product rule stated above.

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Find dy/dx if y=e^2x sin2x ?

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