1. `y=x^3+6x^2-15x+7`
Find Third Derivative

Solution:
`d/(dx)(x^3+6x^2-15x+7)`

`=d/(dx)(x^3)+d/(dx)(6x^2)-d/(dx)(15x)+d/(dx)(7)`

`=3x^2+12x-15+0`

`=3x^2+12x-15`

Now, `d^2/(dx^2)(x^3+6x^2-15x+7)=d/(dx)(3x^2+12x-15)`

`=d/(dx)(3x^2)+d/(dx)(12x)-d/(dx)(15)`

`=6x+12-0`

`=6x+12`

Now, `d^3/(dx^3)(x^3+6x^2-15x+7)=d/(dx)(6x+12)`

`=d/(dx)(6x)+d/(dx)(12)`

`=6+0`

`=6`