What is the first derivative of y= (4x^2 + 2x)/x^2. Can this be done without using the quotient rule.

Given that:

y= (4x^2 - 2x) /
x^2

We need to find the first derivative
y'.

First we will simplify the
expression.

We will factor x from the
numerator.

==> y= x*(4x + 2) /
x^2

Now we will reduce
x.

==> y= (4x+2)/x

Now
we will rewrite :

==> y= 4x/x +
2/x

==> y= 4 + 2/x

Now
we will find the derivative.

==> y' = 0 -
2/x^2

==> y' =
-2/x^2