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

1 Answer
Teddy
Jun 25, 2018

#dy/dx=e^2(sin(2x)+2xcos(2x))#

Explanation:

I'm assuming the function is #y=e^2xsin(2x)#.
#dy/dx=d/dx(e^2xsin(2x))=e^2d/dx(xsin(2x))#
To differentiate #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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