Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

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

13,026 questions

17,572 answers

1,432 comments

33,495 users

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

0 votes

f(x) =(x3 − 5x2 − 4x )/ x1/2

asked Sep 15 in PRECALCULUS by anonymous
reshown Sep 15 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 1 week ago by johnkelly Apprentice
reshown 1 week ago 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
...