Implicit Differentiation.....Huh?

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In class on Thursday, Mr. Bearss introduced a new concept in Calculus called Implicit Differentiation. Which is a fancy way of saying, "Find the derivative of y in respects to x." Now this is a rather confusing topic if I say so, so I figured why not find some practice problems for myself and everyone else. Here are just a few problems to practice with, please post your answers below......

1)x² + y² = 25

2) x³ + y³ = 4

3) y = x² y³ + x³ y²

4) x² + (y-x)³ = 9

And lastly....

5) (x-y³)/(y+x²)=x+2

A Calculus Controversy

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Many moons ago Isaac Newton and Gottfried Leibniz both claimed to have invented calculus. The feud began small, but then erupted into something much more. The math world became divided and sides were chosen. Do some research and see exactly how this quarrel developed.

Questions?

Photo by: JayMay

There have been many topics introduced in class, are there any questions or comments about derivatives, limits, or second derivatives? Also try and find an occupation that uses some or all of these tools!