Question

How do you differentiate `f(x)= ( 4- 3 secx )/ (x -3)` using the quotient rule?

Answer 1

`-(4-3sec(x)-9sec(x)tan(x)+3xsec(x)tan(x))/(x-3)^2`

Explanation:

since `sec(x)=1/cos(x)=(cos(x))^(-1)` we get
we get by the Quotient rule`(-3(-1)(cos(x))^2(-sin(x))(x-3)-(4-3sin(x)))/(x-3)^2`
this simplifies to the term above.