Question

How do you differentiate `f(x)= ( 4- 3 secx )/ (3x + 1)` using the quotient rule?

Answer 1

`f'(x) = (-9xtanxsecx - 3tanxsecx - 12 + 9secx)/(9x^2 + 6x + 1)`

Explanation:

Let's start by finding the derivative of the numerator, since it is somewhat complex and we will need it to apply the quotient rule.

`d/dx(4 - 3secx) = d/dx(4) - d/dx(3/cosx) = 0 - (0 xx cosx - (-sinx xx 3))/cos^2x = -(3sinx)/cos^2x =- 3tanxsecx`

We can now go on with the quotient rule on `f(x)`.

`f'(x) = (-3tanxsecx(3x + 1) - 3(4 - 3secx))/(3x + 1)^2`

`f'(x) = (-9xtanxsecx - 3tanxsecx - 12 + 9secx)/(9x^2 + 6x + 1)`

Hopefully this helps!