Price elasticity of demand calculus

[uwulislis]

I need some help for my math investigation on the price elasticity of demand, I am not sure how these two formulas link together, they are both equations for PED, but how does the variable from the first equation changes to the second one?
First equation

Second equation:

 

[Harry_the_cat]

Quantity(q) is a function of price(p), so let q=f(p).

Because of the way calculus was founded (by Newton and Liebniz at about the same time), two different notations are still used today.

If q=f(p), then the first derivative can be symbolised as $\displaystyle \frac{dq}{dp}$ or as $\displaystyle f ' (p)$.

So, $\displaystyle \frac{dq}{dp}\frac{p_0}{q_0} = f ' (p) \frac{p_0}{f(p_0)}$.

They are both saying the same thing, just in a different language.

 

[JeffM]

Note that there is a slight error in both final results. Elasticities are defined as non-negative quantities. The derivative of a normal demand function is non-positive. The absence of absolute value indicators is an error.