1. ## Differentiation problem

ax1a-1x21-a/(1-a)x1ax2-a = p1/p2

Hey guys. Stuck with this problem as I have forgotten my differentiation rules. I want to be able to show how to cancel down the equation so that it reads

a/(1-a) . x2/x1 = p1/p2

It would be great if someone could give me a step by step breakdown and remind me which rules I need to use here. Thank you

(sorry I didnt know how to use the mathematical script)

2. ## Re: Differentiation problem

Originally Posted by oh507
ax1a-1x21-a/(1-a)x1ax2-a = p1/p2

Hey guys. Stuck with this problem as I have forgotten my differentiation rules. I want to be able to show how to cancel down the equation so that it reads

a/(1-a) . x2/x1 = p1/p2

It would be great if someone could give me a step by step breakdown and remind me which rules I need to use here. Thank you

(sorry I didnt know how to use the mathematical script)
It is not a derivative rule you need, but the law of exponents.

$\displaystyle \frac{a^{m}}{a^n}=a^{m-n}$ and $\displaystyle a^{-m}-\frac{1}{a^m}$

So you have

$\displaystyle \frac{ax_{1}^{a-1}x_{2}^{1-a}}{(1-a)x_1^{a}x_2^{-a}}=\frac{ax_{1}^{-1}x_2^{-1}}{(1-a)}=\frac{a}{(a-1)x_1x_2}$

3. ## Re: Differentiation problem

Hi oh507,

For this problem you don't need any differentiation rules. You need the rules about exponents to simplify the equation. Specifically you will need:

$\displaystyle x^{m} x^{n} = x^{m+n}$

and

$\displaystyle x^{-m} = \frac{1}{x^{m}}$

or

$\displaystyle \frac{1}{x^{-m}} = x^{m}$