Calculus
posted by Charles on .
How is 2cos(4x) the derivative of f(x)=sin(2x)cos(2x)?

If you take the derivative of sin2xcos2x, you get a form of cos^2 2x + sin^2 2x, then you use the double angle formulas to get cos4x

You can also start with identity
f(x) = sin 2x cos 2x = (1/2) sin 4x
Then take the derivative with respect to x. Using the chain rule with u(x) = 4x,
df/dx = df/du du/dx
you get
df/dx = (1/2) cos (4x) *4 = 2 cos (4x) 
drwls: thanks for your help. would you mind explaining how you used that identity to set up the new problem? i get the chain rule but i had no idea that sin2xcos2x was equal to 1/2sin4x. thanks again.