Homework Help

find the derivative of  f(x)=(2-x)^3/(3-x)^2

user profile pic

alexa0048 | Student, Grade 11 | eNoter

Posted January 22, 2013 at 4:34 PM via web

dislike 1 like

find the derivative of  f(x)=(2-x)^3/(3-x)^2

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 22, 2013 at 5:17 PM (Answer #1)

dislike 0 like

The derivative of f(x)=`(2-x)^3/(3-x)^2` has to be determined.

Using the quotient rule:

f'(x) = `(((2-x)^3)'*(3-x)^2-(2-x)^3*((3-x)^2)')/((3-x)^2)^2`

= `(-3*(2-x)^2*(3-x)^2-(2-x)^3*-2*(3-x))/((3-x)^2)^2`

= `(-3*(2-x)^2*(3-x)+(2-x)^3*2)/(3-x)^3`

= `((2-x)^2*(-9 + 3*x +4 - 2x))/(3-x)^3`

= `((2-x)^2*(-5 + x))/(3-x)^3`

= `(x^3-9*x^2+24*x-20)/(3-x)^3`

The required derivative is `(x^3-9*x^2+24*x-20)/(3-x)^3`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes