# what is the derivative of 2sinxcosx? explain please?

You use the product rule, which says for all functions A, B whose derivative you know:

if f(x) = A*B, then f'(x) = A*B’ + A’*B

So, for f(x) = 2sin(x)cos(x), you can choose A = 2sin(x) and

B = cos(x)

It doesn’t matter which one you label A or B. It also doesn’t matter which one has the 2 on the front.

A’ = 2cos(x); B’ = -sin(x)

so f ‘(x) = 2sin(x)*-sin(x) + 2cos(x)cos(x)

= -2(sin(x))^2 + 2(cos(x))^2

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