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

1 Answer
Jun 18, 2018

f'(x) = cos(x)cos(5x)−5sin(x)sin(5x)

Explanation:

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)