if f(x)=(2x)/(4x-3) Find each of the following in simplest form

Question

A. f(x+h)-f(x)/h

B. f(b)-f(a)/b-a

Answer 1

f'(x) = denominator times derivative of numerator minus numerator times derivative of denominator all divided by denominator squared = (dn' - nd')/d^2 = (4x-3)(2) -2x(4))/(4x-3)^2 = (8x-6 -8x)/(4x-3)^2

= -6/(4x-3)^2

do the same with f(x-h)-f(x)/h as h approaches zero, you get the same answer

part b has b-a =h, otherwise the same situation, same solution