How do you use the product rule to differentiate $y = cos (x) \cdot sin (x)$ $y=cos(x)*sin(x)$ ?

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Answer 1 · 2014-10-20T00:33:59

$y = u \cdot v = cos (x) \cdot sin (x)$ $y=u*v=cos(x)*sin(x)$

$u'=-sin(x)$

$v'=cos(x)$

$y'=(uv)'=u'v+uv'=-sin(x)*sin(x)+cos(x)*cos(x)$

$y'=(uv)'=u'v+uv'=-sin^2(x)+cos^2(x)$

How do you use the product rule to differentiate y=cos(x)*sin(x)y=cos(x)⋅sin(x)y=cos(x)*sin(x) ?