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

1 Answer
Feb 11, 2016

#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#