Home > Calculus > Relationship between First and Second Derivatives of a Function

What is the second derivative of #f(x)=cos(-x)#?

Answer 1

#-cos(-x)#

You can compute this in two ways: either you observe that #cos(-x)=cos(x)#, and so you have

#f(x)=cos(x)# #f'(x)=-sin(x)# #f''(x)=-cos(x)#

Or you use the chain rule and compute

#f(x)=cos(-x)# #f'(x)=-sin(-x) * d/dx (-x) = -sin(-x) * -1 = sin(-x)# #f''(x)=cos(-x) * d/dx (-x) = cos(-x) * (-1) = -cos(-x)#

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Answer 2

Ezekiel Alexander

The second derivative of ( f(x) = \cos(-x) ) is ( f''(x) = \cos(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.