If 4y4−5x2y2+x4=0, find δyδy.
This is a typical implicit differentiation problem.
The solution shows that the derivative depends on the values of both
y, but how do students understand this?
In this example, we extend the power of visualization to problems of this sort.
y=-x/2. The CAS factor command gives us a way to verify this.
1 Algebra, and select
4 Factor. Then tap on the history and drag back up to your original expression. Tap on it to select it and then tap
1. How do we reconcile this with the rational expression we have for our derivative?
In this example, we extended the power of visualization to include a polynomial in
The graph of the polynomial led to a better understanding of its derivative and to a conjecture
regarding its properties, and the power of the CAS let us prove the conjecture.
HP Prime, with its CAS and the Advanced Graphing app, represents a new standard in classroom tools to explore
mathematics, make conjectures, and pursue proofs.