find derivative of g(s)= 12s+4/ s+1

Question

how to find the derivative of a function?

Answer 1

Given g(s) = 12s+4/s+1

Apply derivative to each side with respect of s.

d/ds(g(s)) = d/ds[(12s+4)/(s+1)]

Remember the formula d/dx u/v = (vdu/dx-udv/dx)/v^2

Here u = 12s+4, v = s+1

= [(s+1)d/ds(12s+4)-(12s+4)d/ds(s+1)]/(s+1)^2

= [(s+1)12-(12s+4)1]/(s+1)^2

= [12s+12-12s-4]/(s+1)^2

= 8/(s+1)^2

Derivative of g(s) is 8/(s+1)^2.