Question

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

Answer 1

`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.