Question

How do you differentiate `f(x)= ( 4- secx )/ (x + 1)` using the quotient rule?

Answer 1

`(df)/dx=(secx-4-secxtanx(x+1))/(x+1)^2`

Explanation:

According to quotient rule, if `f(x)=g(x)/(h(x))`, then

`(df)/dx=(h(x)xxg'(x)-g(x)xxh'(x))/(h(x))^2`

Hence as `f(x)=(4-secx)/(x+1)`

`(df)/dx=((x+1)(-secxtanx)-(4-secx))/(x+1)^2`

= `(secx-4-secxtanx(x+1))/(x+1)^2`