Find the differential dy given y xx2 3 y x 87x 5 y xx2

Find the differential dy, given: y = -x(x^2 + 3) y = (x - 8)(7x + 5) y = x/x^2 + 1

Solution

a)   y = - x ( x^2 + 3 )

y = -x^3 - 3x

dy = f\'(x) dx

f\'(x) = - 3x^2 - 3

dy = ( -3x^2 - 3 ) dx

b) y = ( x-8 ) ( 7x+5)

y = 7x^2 + 5x -56x - 40

y = 7x^2 - 51x - 40

dy = f\'(x) dx

f\'(x) = 14x - 51

dy = (14x-51) dx

c) y = x / (x^2 + 1)

dy = f\'(x) dx

f\'(x) = (1-x^2) / ( x^2+1)^2

dy = (1-x^2) / ( x^2+1)^2 dx