It is not necessarily the case that a function will be written explicitly in terms of it’s independent variable. In these situations there is usually an expression that involves the independent variable(s) and the dependent variable implicitly. In this case something called implicit differentiation is used when evaluating the derivative. Below is an introduction to implicit differentiation and some practice exercises to really help train the technique of implicit differentation.
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Solving linear relationships involves determining what the value of the variable is. I will usually tell students the first step is to move everything with a variable on one side of the equal sign and all the numbers to the other side of the equal sign.