Find the second derivative

Question

Find the second derivative of y=(x⁵-2x³-3)/x²

Answer 1

y=(x^5-2x^3-3)/x^2

move the denominator to the numerator,

change the sign of its exponent

y= (x^5-2x^3-3)(x^-2)

use the product rule, twice

(ab)' =ab'+ba'

(ab)"= ab"+b'a'+a'b'+ba"

=ab"+2a'b'+ba"

dy/dx=y' = -2(x^5-2x^3-3)/x^3 +(5x^4-6x^2)/x^2

y"=6(x^5-2x^3+5)/x^4 +4(5x^4-6x^2)/x^3 +(20x^3-12x)/x^2

=(46x^5-48x^3+5)/6x^4

=23x/3 -8/x +5/6x^4