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How do you graph the derivative of #f(x) = cos(x)#?

Answer 1

William Abdalla

#f(x) = cosx => f'(x) = -sinx #

This is the graph of #y=f(x)#

And this is a graph of its derivative #y=f'(x)#

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Answer 2

Elijah Abram

To graph the derivative of ( f(x) = \cos(x) ), follow these steps:

Differentiate ( f(x) = \cos(x) ) to find its derivative, which is ( f'(x) = -\sin(x) ).
Plot the function ( f'(x) = -\sin(x) ) on the same coordinate system as ( f(x) = \cos(x) ).
Use the properties of ( \sin(x) ) to understand its behavior. The sine function oscillates between -1 and 1 as ( x ) varies.
Identify critical points where ( f'(x) = 0 ) or is undefined.
Sketch the graph of ( f'(x) ) accordingly, paying attention to the intervals where it is positive, negative, increasing, or decreasing.

This will give you the graph of the derivative of ( 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.