Posted by **Charles** on Sunday, September 28, 2008 at 5:11pm.

How is 2cos(4x) the derivative of f(x)=sin(2x)cos(2x)?

- Calculus -
**bobpursley**, Sunday, September 28, 2008 at 5:57pm
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

- Calculus -
**drwls**, Sunday, September 28, 2008 at 6:19pm
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)

- Calculus -
**Charles**, Sunday, September 28, 2008 at 7:44pm
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.

## Answer this Question

## Related Questions

- Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
- Math - Solving Trig Equations - What am I doing wrong? Equation: sin2x = 2cos2x ...
- calculus - Could someone check my reasoning? thanx Find the derivative of the ...
- Math, derivatives - f(x) = x² + 2Cos²x, find f ' (x) a) 2(x+cos x) b) x - sin x ...
- trig - I dont understand this. can you please tell how you got each answer? ...
- Math - Solving for Trig Equations - Solve the following equation for 0 less than...
- calculus - Differentiate both sides of the double angle identify sin 2x= 2 sin x...
- Calculus I - Find the derivative of f(x) = sin^2 (e^sin^2 x) I wonder if I'm ...
- Pre-Cal - verify the identity sin x(1 - 2 cos^2 x + cos^4 x) = sin^5 x 1-2cos^2 ...
- Math - Calculus - The identity below is significant because it relates 3 ...