Question

Y

=
x
/
3
x
/
2
6
x
+
5
/
3

Answer 1

Y
`=x^2-x-6\\`

Explanation:

y
`=(x^(3) )/(3)- (x^(2) )/(2) -6x+(5)/(3)`

Take the derivation of both sides

y
`=(d)/(dx) ((x^3 )/(3) -(x^2)/(2) -6x+(5)/(3) )`

Write all numerators above the common denominator

y
`=(d)/(dx) ((x^3+5 )/(3) -(x^2)/(2) -6x+(5)/(3) )`

y
`=(d)/(dx) ((x^3+5 )/(3) -(x^2)/(2) -6x )`

y
`=(d)/(dx) ((x^3+5)/(3))-(d)/(dx) ((x^2)/(2))+(d)/(dx) (-6x )`

y
`=(1)/(3)*3x^2-(d)/(dx) ((x^3+5)/(3))-(d)/(dx) ((x^2)/(2))+(d)/(dx) (-6x )`

y
`=(1)/(3)*3x^2-(1)/(2)*2x+(d)/(dx) (-6x)`

y
`=(1)/(3)*3x^2-(1)/(2)*2x-6`

Simplify the expression

y
`=x^2-x-6`