High School Calculus/Implicit Differentiation

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Implicit Differentiation
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When a functional relation between x and y cannot be readily solved for y, the preceding rules may be applied directly to the implicit function.

The derivative will usually contain both x and y. Thus the derivative of an algebraic function, defined by setting the polynomial of x and y to zero.

Ex. 1

Given the function y of x



In solving for we must first factor the differentiation problem

In doing this we get

From here we subtract the to one side

Thus giving us

Here I am going to skip a step in solving this implicit differentiation problem. I am going to skip the step where I divide the -1 over to the other side.

From here we divide the polynomial from the over to the other side. Giving us

Now we simplify and get

Other problems to work on

Ex. 2

Find given the function

Ex. 3

Find given the function