Question

Differentiate f(x) = (5x³+7x )/(2x²-4x+5 ) using quotient rule.

Answer 1

$f'(x)=\left(\frac{5x^3+7x}{2x^2-4x+5}\right)'=\\ {}=\frac{(5x^3+7x)'(2x^2-4x+5)-(5x^3+7x)(2x^2-4x+5)'}{(2x^2-4x+5)^2}=\\ {}=\frac{(15x^2+7)(2x^2-4x+5)-(5x^3+7x)(4x-4)}{(2x^2-4x+5)^2}=\\ {}=\frac{10x^4-40x^3+61x^2+35}{(2x^2-4x+5)^2}.$