what-is-implicit-differentiation-kristakingmath

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Most often in calculus, you deal with explicitly defined functions, which are functions that are solved for y in terms of x. In that case, finding the derivative is usually really simple, because you just call the left-side of the equation y', and then you differentiate the right side with respect to x.

But when you come across an implicitly defined function, finding the derivative isn't always that easy. Implicit functions are functions where the x and y variables are all mixed up together and can't be easily separated. That's when implicit differentiation comes in handy.

Implicit differentiation lets us take the derivative of the function without separating variables, because we're able to differentiate each variable in place, without doing any rearranging.

When we use implicit differentiation, we differentiate both x and y variables as if they were independent variables, but whenever we differentiate y, we multiply by dy/dx. That's because y, as a dependent variable, is actually a function of x. Therefore, when we take its derivative, it's as if we're taking the derivative of a composite function, and we therefore have to apply chain rule. When we do apply chain rule, we multiply by the derivative of y, which is dy/dx.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

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Tagged under: implicit differentiation,chain rule,composite functions,Krista King, implicit differentiation works,educational,calculus, implicit differentiation, implicit differentiation

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