Find the derivative of the function.
Using product rule,
= [sin(5x)]' cos(2x) + sin(5x)[cos(2x)]'
= 5cos(5x) cos(2x) - 2sin(5x) sin(2x)
Thank you. I was wondering if you can go any farther and make it -2sin2 10x2 + 5cos2 10x2
It is tempting to go further, but since 5x and 2x are different arguments of cosine or sine you cannot combine them that way.
If you had an expression like 5 cos(2x)cos(2x) - 2 sin(5x)sin(5x) you
would be able to combine to express it as 5 cos^2(2x) - 2 sin^2(5x).
thank you so much! I understand now!