Differentiation of Trig Funcns
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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

© Matthew Pinkey

Other Notes in this Category

1. Chain, Product and Quotient
2. Differential Equations
3. Differentiation
4. Differentiation from 1st Principles
5. Differentiation of Trig Funcns
6. Exponentials & Logarithms
7. Implicit Differentiation
8. Integration
9. Integration by Parts
10. Integration by Substitution
11. Tangents and Normals
12. The Second Derivative
13. Uses of Differentiation
14. Volumes of Revolution

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