Find the Derivative of the Given Function?

I'm assuming you meant that the answer is (-2x-3)/(2x^2(4x+3)^1/2)

You have to remember the rule for finding the derivative of an equation like that. The rule is that for an equation y=f(x)/g(x), y'=(f'(x)g(x)-g'(x)f(x))/(g(x))^2

Basically, (the derivative of the numerator x the denominator)-(the derivative of the denominator x the numerator) all divided by the denominator^2

It's really easy to get lost throughout this process cuz of all the algebra. For some people, it's simple and doesn't take long. But I'll show you one way to do this.

So, following the rule from above, you should have this

y'=(((1/2((4x+3)^(-1/2))*4))2x)-(2( 4x+3)^1/2) all divided by 4x^2.

You'll have to do some algebra to simplify it. If you get lost in the algebra, it's okay, since it's a rather involved problem. Still, you might want to brush up on some algebra concepts. It'll definitely come in handy.

y = (4x + 3)^1/2 / 2x

Y' = -(4x + 3)^1/2 / 2x^2 + (1/2)(4) / 2x(4x+3)^1/2,

OR,

y' = (1/2x^2(4x+3)^1/2)[-(4x+3) + 2x]

OR,

y' = (-2x-3) / 2x^2 ( 4x+3)^1/2 >==========================< ANSWER