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Create a function that has two x’s and two y’s in it. We will assume that y is a function of x. You may use product rule or quotient rule, but not both. I will post a couple of examples, but let’s keep this fairly simple.
Sample equations: xy + x = 2y – 7;
𝑥
2
𝑦
–
3
=
2
𝑥
+
3
𝑦
2
;
Response Post 1: Implicitly differentiate the function in the main post. ONLY do the first step. But make sure you get all of your dy/dx’s in there. Then, make sure you explain how you know when to use dy/dx and when not to.
Sample Equation:
𝑥
3
𝑦
5
+
3
𝑥
=
8
𝑦
3
+
1
Response Post 2: Take the implicitly differentiated equation and solve for dy/dx.
𝑦
+
cos
(
𝑥
2
)
=
𝑥
𝑒
𝑦
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