**The derivatives of trigonometric functions**

It is possible to find the derivative of trigonometric functions.

Here is a list of the standard forms that you need to know:

__d__ (sin x) = cos x

dx

__d__ (cos x) = - sin x

dx

__d__ (sec x) = sec x tan x

dx

__d__ (cosec x) = -cosec x cot x

dx

__d__ (tan x) = sec²x

dx

__d__ (cot x) = -cosec²x

dx

One condition upon these results is that x must be measured in radians.

**Applying the Chain Rule**

The chain rule is used to differentiate harder trigonometric functions.

Example:

Differentiate cos³x with respect to x.

Let y = cos³x

Let u = cos x

therefore y = u³__dy__ = 3u²

du

__du__ = -sin x

dx

__dy__ = __du__ × __dy__

dx dx du

= -sin x × 3u²

= -sin x × 3cos²x

= -3cos²x sin x

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