Assuming that h(x)=f(x)/g(x) is differentiable, use the product rule to derive the quotient formula.?

Question

[Hint: Differentiate both sides of the equation h(x)*g(x)=f(x) and solve for h'(x).]

Answer 1

h(x)=f(x)/g(x)
h(x) = f(x) * 1/g(x)
h'(x) = [f(x) * -g'(x)/g(x)^2 + f'(x)*1/g(x)]
h'(x) = (g(x)f'(x) -f(x)(g'(x))/g(x)^2

Answer 2

employing quotient rule , dy/dt is given by way of potential of :- [ a million + e^(2t) ] [ 2e^(2t) ] - e^(2t) [ 2e^(2t) ] --------------------------------------..... [ a million + e^(2t) ]^2 a million --------------------- [ a million + e^(2t) ]^2