What is the derivative of 1-cosx?

Answer 1
Answer: #Sin x#

Justification

The derivatives for the #sin# and #cos# functions are interconnected as follows: #d/dx sin(x) = cos(x)# #d/dx cos(x) = -sin(x)# #d/dx -sin(x) = - cos(x)# #d/dx - cos(x) = sin(x)#
(Also worth noting is that #cos (-x) = cos(x)# and #sin(-x) = -sin(x)#, though those will not have bearing here).
With this in mind, taking the derivative of #f(x) = 1-cos(x)# would proceed as follows:
#d/dx (1 - cos(x)) = d/dx (1) + d/dx (-cos(x))# (Recalling that the derivative of a sum/difference is equal to the sum/difference of the derivatives) #= 0 + sin (x)# (recalling that the derivative of a constant is 0) #= sin(x)#
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Answer 2

The derivative of (1 - \cos(x)) is (\sin(x)).

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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.

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.

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.

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.

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