Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,286 questions

17,801 answers

1,438 comments

34,241 users

Find the derivative of the function. f(x) =

0 votes

f(x) =(x3 − 5x2 − 4x )/ x1/2

asked Sep 15, 2018 in PRECALCULUS by anonymous
reshown Sep 15, 2018 by bradely

1 Answer

0 votes

f(x) =(x3 − 5x2 − 4x )/ x1/2

Calculate the derivative of the function using the quotient rule.

d/dx(u/v) =[v(du/dx) −u(dv/dx)]/v^2

f '(x) =[x1/2*d/dx(x3 − 5x2 − 4x ) − (x3 − 5x2 − 4x )*d/dx(x1/2 )] /(x1/2 )^2

         =[x1/2*(3x2 − 10x − 4) − (x3 − 5x2 − 4x)*(1/2)(x−1/2 )] /(x)

        = [(3x5/2 − 10x3/2 − 4x1/2 ) − (x5/2 − 5x3/2 − 4x1/2 )*(1/2)] /(x)

     = [(3x5/2 − 10x3/2 − 4x1/2 ) − (x5/2 − 5x3/2 − 4x1/2 )*(1/2)] /(x)

     = [(5/2)(x5/2) (15/2)(x3/2)(2x1/2)]/x

     =[(5/2)(x3/2) (15/2)(x1/2)(2x-1/2)]

answered Sep 17, 2018 by johnkelly Apprentice
reshown Sep 17, 2018 by bradely

Related questions

asked Jul 19, 2014 in CALCULUS by anonymous
asked Jan 22, 2015 in CALCULUS by anonymous
asked Jan 22, 2015 in CALCULUS by anonymous
asked Jan 21, 2015 in CALCULUS by anonymous
...