Question

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

Answer 1

• Quotient rule: `(a/b)'=(a'b-ab')/b^2`
• We'll also need product rule for `xtanx`, which consists on `(ab)'=a'b+ab'`

Explanation:

`(f(x))/(dx)=((1-(tanx+sec^2x))(x-3)-(x-xtanx))/(x-3)^2`

`(f(x))/(dx)=(cancel(x)-3-cancel(xtanx)+3tanx-xsec^2x+3sec^2x-cancel(x)+cancel(xtanx))/(x-3)^2`

`(f(x))/(dx)=(3(tanx-1)+(3-x)sec^2x)/(x-3)^2`