Differentiate F(x)=(25+v)/v

Whenever there is an equation in the form f(x)=u/w, the quotient rule tells us that:

   f '(x)= [w(du/dx)-u(dw/dx)]/v²  *It looks complecated but if you break it down, it is simple.

All you need is u, v, du/dx and dv/dx, which in this case is:

        u=25+v        w=v²

 du/dx=1        dw/dx=2v      <- All I did was differentiate polynomials differentiation

Sub these into our equation part by part:

w(du/dx)=1*v²=v²    u(dw/dx)=(25+v)*2v=50v+2v² => -u(dw/dx)=-50v-2v²   w²=(v²)²=v⁴

Now sub in:

f '(x)=(v²-50v-2v²)/v⁴=(-50v-v²)/v⁴

Now cancel a v as it occurs in all parts of the equation:

f '(x)=(-50-v)/v³=-(50+v)/v³

And there is our answer, nothing more can be done to it^.