what is the second derivative of this?

Question

f '(x)= ((4x)/(x^2+3))-1

Answer 1

You'll need to use the quotient formula twice. The quotient rule for differentiation states that (f/g)' = (g*f' - f*g') / g^2. Here, f = 4x so f' = 4. g = x^2 + 3 so g' = 2x. The derivative of a constant is zero, so you can essentially ignore the - 1. Once you've found (f/g)', take the derivative again; f and g will now be something different.

Answer 2

f' = u1(x)*u2(x) - 1

f'' = u1*u2' + u2*u1'
u1' = 4
u2' = -2x/(x^2+3)^2