Question

How do you differentiate `f(x)= ( x - 3 secx )/ (x -3)` using the quotient rule?

Answer 1

`f'(x)=(3((3-x)secxtanx+secx-1))/(x-3)^2`

Explanation:

The quotient rule states that

`f'(x)=((x-3)d/dx(x-3secx)-(x-3secx)d/dx(x-3))/(x-3)^2`

The respective derivatives contained within are `d/dx(x-3secx)=1-3secxtanx` and `d/dx(x-3)=1`. We obtain

`f'(x)=((x-3)(1-3secxtanx)-(x-3secx)(1))/(x-3)^2`

We can distribute and simplify.

`f'(x)=(x-3-3xsecxtanx+9secxtanx-x+3secx)/(x-3)^2`

`f'(x)=(3((3-x)secxtanx+secx-1))/(x-3)^2`