# Simple Quotient Derivative

1. Oct 21, 2011

### Nano-Passion

EDIT: I found the mistake, question is answered! Its funny because I spent 40+ minutes trying to get the right answer and looking for the mistake but typing it all out in latex helped me to find it!

1. The problem statement, all variables and given/known data

$$\frac{\sqrt{x}}{x^3+1}$$

3. The attempt at a solution

$$\frac{\sqrt{x}}{x^3+1}$$
$$\frac{d/dx (x^{1/2}(x^3+1))-d/dx(x^{3}+1)x^{1/2}}{(x^3+1)^2}$$
$$\frac{\frac{1/2x^{-1/2}(3x+1)3x^2(x^{1/2}}{(x^3+1)^2}}$$
$$\frac{\frac{x^3+1}{2\sqrt{x}}3x^{5/2}}{(x^3+1)^2}$$
$$\frac{x^3+3x^{5/2}+1}{2\sqrt{x}(x^3+1)^2}$$

But the correct answer is:

$$\frac{1-5x^2}{2\sqrt{x}(x^3+1)^2}$$

Last edited: Oct 21, 2011
2. Oct 21, 2011

### Staff: Mentor

The line above is wrong.

You should have this:
$$\frac{d}{dx}\frac{\sqrt{x}}{x^3+1}$$
$$=\frac{(x^3+1)\cdot d/dx (x^{1/2})- x^{1/2}d/dx(x^{3}+1)}{(x^3+1)^2}$$
Can you continue?

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