Thread: Need help with this derivative?

The funciton is 3x/(x^2+4)
I have no idea how to differentiate it. Step by step instructions would really help.

Use the Quotient Rule.

What's the quotient rule? I know the product rule is f(x)g'(x)+f'(x)g(x)

Originally Posted by AFireInside

What's the quotient rule? I know the product rule is f(x)g'(x)+f'(x)g(x)

If you don't know the Quotient Rule, you can use the Product Rule if you rewrite the function as 3x(x^2 + 4)^(-1)

But what do i do with the -1 exponent?

Originally Posted by AFireInside

But what do i do with the -1 exponent?

You would need to use the chain rule to differentiate (x^2 + 4)^(-1)

But then the -1 becomes a -2 and it doesn't really get you anywhere

Originally Posted by AFireInside

But then the -1 becomes a -2 and it doesn't really get you anywhere

What's wrong with that?

Well using the chain rule (x^2+4)^-1 would become -(x^2+4)^-2 x (x^2+4).
I don't see how that simplifies things.

No it doesn't... It's the derivative of the inside times the derivative of the outside.

Now I'm lost.

The inside is u = x^2 + 4. What is its derivative?

The outside is u^(-1). What is its derivative?

Originally Posted by AFireInside

Well using the chain rule (x^2+4)^-1 would become -(x^2+4)^-2 x (x^2+4). I don't see how that simplifies things.

If then .

I thought chain rule was nf'(x) x f(x)^n-1
So it should be -1(2x)(x^+4)^-2

Correct, despite the typo, it should be -2x(x^2 + 4)^(-2).

So now you can apply the product rule.