Differentiate (3x^2-5x)/(4x^3+2x^2)

We can differentiate the expression using the quotient rule. If f(x)=u(x)/v(x) then f'(x)=(u'(x)v(x)-u(x)v'(x))/v(x)^2. In this case u(x)=3x^2-5x so u'(x)=6x-5 and v(x)=4x^3+2x^2 so v'(x)= 12x^2+4x. Using the quotient rule the full derivative is: (6x-5)(4x^3+2x^2)-(3x^2-5x)(12x^2+4x)/(4x^3+2x^2)^2