Proof of Differentiation Rules

Hint: Find the first derivative of [p(x)]2[q(x)]2[p(x)]^2-[q(x)]^2
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Do I add in some kind of expression that equals zero but that also allows me to rearrange and factor things even further now? Or, would the 2 lead me to the constant I'm looking for?
 
Substitute p(x)p'(x) by q(x)q(x) and q(x)q'(x) by p(x)p(x). What can you conclude from the value of derivative?
 
Substitute p(x)p'(x) by q(x)q(x) and q(x)q'(x) by p(x)p(x). What can you conclude from the value of derivative?
It equals zero? OH, so therefore there must be a constant!! But why must it equal a constant?
 
Take for granted: If f(x)=0f'(x)=0 on (a,b)(a,b) then f(x)f(x) must be constant.
 
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