# Did i find the derivative correctly?

1. May 7, 2006

### dejan

Hi there,
Just wondering if i found dy/dx of (x+1)^2/1+x^2 = 2(x+1)/2x and also the second derivative d^2 y/dx^2=(x+1)/2
Is that correct?? I don't think it is.

2. May 7, 2006

### d_leet

No its not the derivative of a quotient is not equal to the quotient of the derivatives. Have you learned the quotient rule for differentiating these kinds of functions?

3. May 7, 2006

### dejan

Aww i have to use the quotient rule?? *sigh*
Well we didn't go that far:( More work! Thanks anyway!

4. May 7, 2006

### Curious3141

Well, you don't *have* to. You can use one of multiple methods,

for example, partial fraction decomposition into elementary functions with complex factors in the denominator.

Or even substitute $$x = tan \theta$$ simplify with trig identities first, then observe that $$\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$$

There are many way to skin a cat.

5. May 8, 2006

### dav2008

Have you learned the product rule? The quotient rule is just a special case of the product rule.

Your function is a product of $$(x+1)^2$$ and $$(1+x^2)^{-1}$$

Last edited: May 8, 2006
6. May 8, 2006

### dejan

Yeah we've learnt the product rule, chain and all....just that we have to graph that, but doing it without a graphics calculator.
I think i get it now.