# 12.6.1. Derivatives of Trigonometric Functions

Given that the function , discuss its differentiability at any point of its domain.

- AThe function is differentiable on .
- BThe function is differentiable on .
- CThe function is differentiable on .
- DThe function is differentiable on .

Discuss the differentiability of the function at .

- A is differentiable at .
- B is not differentiable at because is discontinuous at .
- C is continuous but not differentiable at because .
- D is not differentiable at because is undefined.

Given that the function , discuss its differentiability at .

- AThe function is not differentiable at because doesn't exist.
- BThe function is not differentiable at because is not continuous at that point.
- CThe function is differentiable at because exists.
- DThe function is differentiable at because exists.

Given that the function , discuss its continuity and differentiability at .

- AThe function is not continuous but differentiable at .
- BThe function is continuous and differentiable at .
- CThe function is continuous but not differentiable at .
- DThe function is not continuous, so it is not differentiable at .

Given that , discuss the differentiability of at .

- AThe function is not differentiable at that point as .
- BThe function is differentiable at that point as .
- CThe function is differentiable at that point as exists.
- DThe function is not differentiable at as is discontinuous at that point.

Given that the function , discuss the differentiability of at .

- AThe function is not differentiable at as is discontinuous at that point.
- BThe function is differentiable at as is continuous at that point.
- CThe function is not differentiable at that point as .
- DThe function is differentiable at that point as .

Given that the function , discuss its differentiability at .

- A is not differentiable at because is undefined.
- B is differentiable at because is continuous at .
- C is not differentiable at because is discontinuous at .
- D is continuous but not differentiable at because .

Given that the function , is differentiable at , find the values of and .

- A, .
- B, .
- C, .
- D, .