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Chain Rule & Integration by Substitution

Many ways problem

Implicit circles
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Problem

Find the gradient of the curve \(x^2+y^2=4\) at the following three points.

A circle with equation x squared plus y squared equals 4, with 3 points marked, root 2 root 2, negative root 3 1, and a half, negative root 15 over 2

What is the derivative, \(\dfrac{dy}{dx}\), at a general point on the curve?