How do you find the derivative of $y=2cosxsinx$

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Answer 1 · 2015-02-25T16:01:18

$2cos(2x)$

Since $y = 2 cos(x) sin(x)$ is the same as
$y = sin (2x)$

and
$(d sin(theta))/(d theta) = cos( theta)$

Let $g(a) = sin(a)$ and $h(b) = 2b$
(So $y = g(h(x))$ )

By the chain rule:
$(d y)/(dx) = (d g(h(x)))/(d h(x)) * (d h(x))/(dx)$

$color(white)((dy)(dx))=(d(sin(2x)))/(d(2x)) * (d(2x))/(dx)$

$color(white)((dy)(dx))= cos(2x) * 2$
or
$color(white)((dy)(dx))= 2 cos(2x)$

How do you find the derivative of y=2cosxsinxy=2cosxsinx