## 3.4 Differentiation Rules for Circular Functions

#### Differentiation Rules for \sin(x), \cos(x), \tan(x)

- The other rules regarding differentiation such as addition, subtraction, multiplication, division of functions, chain rule etc. applies too.
- All of these rules can be proven via first principles, but it is not required.
- The
**basic rules**in this section are:

i) If f(x)=\sin(x), then f^{\prime}(x)=\cos x

ii) If f(x)=\cos x, then f^{\prime}(x)=-\sin x

iii) If f(x)=\tan x, than f^{\prime}(x)=\sec^2x=\sec x \times \sec x

- It is possible to expand these further using chain rule: