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

1 Answer
Jun 25, 2018

dy/dx=e^2(sin(2x)+2xcos(2x))dydx=e2(sin(2x)+2xcos(2x))

Explanation:

I'm assuming the function is y=e^2xsin(2x)y=e2xsin(2x).
dy/dx=d/dx(e^2xsin(2x))=e^2d/dx(xsin(2x))dydx=ddx(e2xsin(2x))=e2ddx(xsin(2x))
To differentiate xsin(2x)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.