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

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Answer 1 · 2015-10-22T22:56:24

See the explanation.

Before learning the chain rule, you need to use a fact from trigonometry:

$cos (- x) = cos x$ $cos(-x) = cosx$

Therefore,

$\frac{d}{d x} (cos (- x) = \frac{d}{d x} (cos x) = - sin x$ $d/dx(cos(-x) = d/dx(cosx) = -sinx$

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

Using the chain rule

$\frac{d}{d x} cos (- x) = - sin (- x) \cdot \frac{d}{d x} (- x)$ $d/dx cos(-x) = -sin(-x)*d/dx(-x)$

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

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