`y=-1/4x^8+1/2x^4-3^2`

Differentiating term by term, we have:

`d/(dx)(-1/4x^8)=-8/4x^7=-2x^7`

`d/(dx)(1/2x^4)=4/2x^3=2x^3`

`d/(dx)(3^2)=0` (this is the derivative of a constant)

So

`(dy)/(dx)=d/(dx)(-1/4x^8+1/2x^4-3^2)` `=-2x^7+2x^3`

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