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How do you find the derivative of #cos(-x)#?

Answer 1

Elijah Abram

See the explanation.

Prior to studying the chain rule, you must apply the following trigonometric fact:

#cos(-x) = cosx#

Consequently,

#d/dx(cos(-x) = d/dx(cosx) = -sinx#

(By the way #sin(-x) = -sinx#, so the answer couls be written #sin(-x)#.

Applying the rule of chain

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

# = -sin(-x)(-1) = sin(-x) = -sinx#

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Answer 2

Emily Ammerman

To find the derivative of cos(-x), apply the chain rule. The derivative of cos(-x) is sin(-x) multiplied by the derivative of -x, which is -1. Thus, the derivative of 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.