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

1 Answer
Mar 15, 2018

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

Explanation:

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

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