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

1 Answer
Jan 6, 2016
  • 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