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

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Answer 1 · 2017-06-10T22:11:21

Never forget that $cos^2x = (cosx)^2$ .

$y = sinxcos^2x$

is a product $y = uv$
Its derivative is $y' = u'v+uv'$

To differentiate $v = cos^2x$ , we'll need the chain rule.
$d/dx(cos^2x) = 2cosx d/dx(cosx) = 2cosx(-sinx) = -2sinxcosx$

$y' = d/dx(sinxcos^2x) = (cosx)(cos^2x)+(sinx)(-2sinxcosx)$

$= cos^3x - 2sin^2xcosx$ .

You may rewrite this answer to taste.

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