What is the derivative of $sin^2(x)$ ?

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Answer 1 · 2016-01-09T06:40:43

The derivative is $2sin(x)cos(x)$ or it can also be written as $sin(2x)$

$y=sin^2(x)$

Let us use the chain rule.

Let $y=u^2$ and $u = sin(x)$

Chain rule:

$dy/dx = dy/(du)xx(du)/dx$

$y=u^2$

$dy/(du) = 2u$

$u=sin(x)$

$(du)/dx = cos(x)$

$dy/dx = dy/(du)xx(du)/dx$

$dy/dx = 2uxxcos(x)$

$dy/dx = 2sin(x)cos(x)$

$dy/dx = sin(2x)$

What is the derivative of sin^2(x)sin^2(x)?