Question

How do you differentiate `f(x) = (x^2-4x)/(xcotx+1)` using the quotient rule?

Answer 1

`(df)/dx=((2x-4)(xcotx+1)+(x/sin^2theta-cotx)(x^2-4x))/(xcotx+1)^2`

Explanation:

`(df)/dx=((d(x^2-4x))/dx(xcotx+1)-(d(xcotx+1))/dx(x^2-4x))/(xcotx+1)^2=`

`((2x-4)(xcotx+1)-(-x/sin^2theta+cotx)(x^2-4x))/(xcotx+1)^2=`

`((2x-4)(xcotx+1)+(x/sin^2theta-cotx)(x^2-4x))/(xcotx+1)^2`