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`

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2. `y=x^4-9x^2+24x+2`
Find Third Derivative

Solution:
`=x^4-9x^2+24x+2`

`d/(dx)(x^4-9x^2+24x+2)`

`=d/(dx)(x^4)-d/(dx)(9x^2)+d/(dx)(24x)+d/(dx)(2)`

`=4x^3-18x+24+0`

`=4x^3-18x+24`

Now, `d^2/(dx^2)(x^4-9x^2+24x+2)=d/(dx)(4x^3-18x+24)`

`=d/(dx)(4x^3)-d/(dx)(18x)+d/(dx)(24)`

`=12x^2-18+0`

`=12x^2-18`

Now, `d^3/(dx^3)(x^4-9x^2+24x+2)=d/(dx)(12x^2-18)`

`=d/(dx)(12x^2)-d/(dx)(18)`

`=24x-0`

`=24x`

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3. `y=4x^5+19x^3-14x+3`
Find Third Derivative

Solution:
`=4x^5+19x^3-14x+3`

`d/(dx)(4x^5+19x^3-14x+3)`

`=d/(dx)(4x^5)+d/(dx)(19x^3)-d/(dx)(14x)+d/(dx)(3)`

`=20x^4+57x^2-14+0`

`=20x^4+57x^2-14`

Now, `d^2/(dx^2)(4x^5+19x^3-14x+3)=d/(dx)(20x^4+57x^2-14)`

`=d/(dx)(20x^4)+d/(dx)(57x^2)-d/(dx)(14)`

`=80x^3+114x-0`

`=80x^3+114x`

Now, `d^3/(dx^3)(4x^5+19x^3-14x+3)=d/(dx)(80x^3+114x)`

`=d/(dx)(80x^3)+d/(dx)(114x)`

`=240x^2+114`

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