what is the derivative of 2sinxcosx in a form of AcosBx

Question

i need to know this derivative i need it quikly please

Answer 1

Another way to solve this:

 

d/dx (2 sinx cox) = 2(cos²x - sin²x)

 

Use the identity  

 

cos²x - sin²x = cos(2x)

 

d/dx (2 sinx cosx) = 2cos(2x)

 

But it is simpler to first replace 2sinx cosx with sin(2x), and then differentiate.

Answer 2

2sinxcosx = sin2x (a trig identity, easily proven using the sin sum formula)

Thus, the derivative is 2cos2x