# Find dy/dx, dy2/dx, dy3/dx for the following functions 1) y = 3x = 5 2) y = 3x2 – 5 3) y = 3x1/3 4) y = 3x4 – 6x-1/3

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### 1 Answer

1)`(dy)/(dx)= 3`

`(d^2y)/((dx)^2)=0`

`(d^3y)/((dx)^3)=0`

2) `(dy)/(dx)= 6x`

`(d^2y)/((dx)^2)=6`

`(d^3y)/((dx)^3)=0 `

3) `y=3x^(1/3)`

`(dy)/(dx)= 3(1/3)x^(1/3-1)=x^(-2/3)`

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

`(d^3y)/((dx)^3)=(-2/3)(-5/3)x^(-5/3-1)=10/9x^(-8/3)`

4)`y=3x^4-6x-1/3`

`(dy)/(dx)= 3*4x^3-6=12x^3-6`

`(d^2y)/((dx)^2)=12*3x^2`

`(d^3y)/((dx)^3)=36*2x=72x`