1. `y=x^7+6x^3-15x+7`
Find nth Derivative / Higher order Derivative

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

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

`=7x^6+18x^2-15+0`

`=7x^6+18x^2-15`

Now, `d^2/(dx^2)(x^7+6x^3-15x+7)=d/(dx)(7x^6+18x^2-15)`

`=d/(dx)(7x^6)+d/(dx)(18x^2)-d/(dx)(15)`

`=42x^5+36x-0`

`=42x^5+36x`

Now, `d^3/(dx^3)(x^7+6x^3-15x+7)=d/(dx)(42x^5+36x)`

`=d/(dx)(42x^5)+d/(dx)(36x)`

`=210x^4+36`

Now, `d^4/(dx^4)(x^7+6x^3-15x+7)=d/(dx)(210x^4+36)`

`=d/(dx)(210x^4)+d/(dx)(36)`

`=840x^3+0`

`=840x^3`

Now, `d^5/(dx^5)(x^7+6x^3-15x+7)=d/(dx)(840x^3)`

`=2520x^2`

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2. `y=4x^5+19x^3-14x+3`
Find nth Derivative / Higher order 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`

Now, `d^4/(dx^4)(4x^5+19x^3-14x+3)=d/(dx)(240x^2+114)`

`=d/(dx)(240x^2)+d/(dx)(114)`

`=480x+0`

`=480x`

Now, `d^5/(dx^5)(4x^5+19x^3-14x+3)=d/(dx)(480x)`

`=480`

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