Question

How do you differentiate `f(x)= ( -2x^2+ 3x ) / ( 4e^x + 2 )` using the quotient rule?

Answer 1

Set `u(x)=-2x^2+3x` and `v(x)=4e^x+2` then the quotient rule

says that the first derivative of `f(x)=(u(x))/(v(x))` is

`f'(x)=(u'(x)*v(x)-u(x)*v'(x))/(v(x)^2)`

where `u'(x)=-4x+3` and `v'(x)=4*e^x`