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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

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