How do you differentiate f(x)=(2x^2-x+1)/(2x-1)f(x)=2x2x+12x1 using the quotient rule?

1 Answer

f^'(x)=[4x^2-4x-1]/[(2x-1)^2]

Explanation:

Quotient rule states that if h and k are two differentiable functions on ]a,b[, then forall x in ]a,b[ such that k(x) ne 0 the following equality holds:
[(h(x))/(k(x))]^'=[h^'(x)k(x)-h(x)k^'(x)]/(k^2(x))

In our case h(x)=2x^2-x+1 and k(x)=2x-1. The two derivatives are h^'(x)=4x-1 and k^'(x)=2.
f^'(x)=[(4x-1)(2x-1)-(2x^2-x+1)2]/[(2x-1)^2]=[8x^2-6x+1-4x^2+2x-2]/[(2x-1)^2]=[4x^2-4x-1]/[(2x-1)^2]