`F(v)=(v/(v^3+1))^6`

`F(v)=v^6(v^3+1)^-6`

By applying product rule of derivative,

`F'(v)=v^6 d/(dv) (v^3+1)^-6 + (v^3+1)^-6 d/(dv) v^6`

`F'(v)=v^6(-6)(v^3+1)^-7(3v^2) + (v^3+1)^-6 (6v^5)`

`F'(v)=-18v^8(v^3+1)^-7 + 6v^5(v^3+1)^-6`

`F'(v)=(-18v^8)/(v^3+1)^7 + (6v^5)/(v^3+1)^6`

`F'(v)=(-18v^8+6v^5(v^3+1))/(v^3+1)^7`

`F'(v)=(-18v^8+6v^8+6v^5)/(v^3+1)^7`

`F'(v)=(-12v^8+6v^5)/(v^3+1)^7`

`F'(v)=(6v^5(1-2v^3))/(v^3+1)^7`

**Note:- 1) If y = x^n ; then dy/dx = n*{x^(n-1)}**

**2) If a function to be differentiated contains sub-functions,then by the rule of differentiation, the last function is differentiated first.**

**3) If the function is of the form y = u/v ; where u & v are both functions of 'x' , then dy/dx = y' = [{v*u' - u*v'}/(v^2)]**

Now, for the given question , find the solution in the attachment