How do you differentiate # f(x) =2cosx+sin2x #?

1 Answer
Mar 15, 2018

#2cos(2x) -2sin(x) #

Explanation:

the derivative of #cos(x)# is defined as #-sin(x)#
therefore for the first term, the derivative of a constant multiplied by #cos(x)# gives that same constant multiplied by #-sin(x)#

therefore derivative of the first term is
#-2sin(x)#

the derivative of the second term can be found by using The Chain Rule

#d/dx f(g(x)) = f'(g(x))*g'(x)#

therefore,
let #f(x) = sin(x)#
and #g(x) = 2x#

therefore,
#d/dx f(g(x)) = d/dx sin(2x) = f'(g(x))*g'(x) = cos(2x)*2#

#= 2cos(2x)#

therefore, the entire derivative is,
#-2sin(x) + 2cos(2x)#
=