What is the derivative of #sin( x ) cos( 5 x )#?

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Answer 1 · 2018-06-18T08:31:59

#f'(x) = cos(x)cos(5x)−5sin(x)sin(5x)#

#f(x) = sin(x)cos(5x)#

The product rule states that:

If #f(x) = u(x)xxv(x)#

Then #f'(x) = u(x)v'(x) + v(x)u'(x)#

In this example: #u(x) = sin(x) and v(x) = cos(5x)#

#u'(x) = cos(x)#

#v'(x)= -sin(5x).5# [Chain rule]

#:. f'(x) = sin(x).(-5sin(5x)) + cos(5x).cos(x)#

#= cos(x)cos(5x)−5sin(x)sin(5x)#