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

Answer 1

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

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)# =

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Answer 2

Luke Alvarez

To differentiate ( f(x) = 2\cos(x) + \sin(2x) ), use the chain rule and the derivative formulas for cosine and sine functions.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.