Implicit Differentiation
Introduction
Implicit Differentiation is a way to take derivatives when your function is not of the form y = "expression of one variable". It is a application of the chain rule, and can make differentiation much simpler.
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Whenever you implicitly differentiate you have to pay attention to the different variables. If you are taking the derivative with respect to x, and the term has an x in it, you do the regular derivative.
If the term has another variable instead of x, for example y. You take the derivative with respect to y, then multiply it by dy/dx.
In essence, it's just one extra step of multiplying the derivative by dy/dx.
Once you have finished doing this, you gather dy/dx to one side of the equation, and that is the derivative y with respect to x.
Note:
At times, the notation y' will be used instead of dy/dx.
The video above explains the different uses, and shows how to carry out the steps.
Preview - Members Only Practice
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