► My Derivatives course: https://www.kristakingmath.com/derivatives-course
Implicit differentiation is the method you use to find a derivative when you can't define the original equation explicitly. Explicitly defined equations are equations that are solved for y in terms of x. In other words, equations in which the x and y variables are separated. If you can't separate the x and y variables, and you still need to take the derivative, then implicit differentiation is how you do it.
To use implicit differentiation, you can treat both variables like you would normally treat the independent variable x. In other words, whenever you come across y, you take the derivative with respect to y, and whenever you come across x, you take the derivative with respect to x. The caveat is that you always have to multiply by dy/dx, or y', whenever you take the derivative with respect to y. The reason is because you can't actually take the derivative with respect to y, since x is the independent variable. Instead, you have to take the derivative with respect to x, and since y is a function of x, when you take the derivative of y, you always have to multiply by dy/dx.
Once you've taken the derivative of both sides of the equation, you'll need to solve for dy/dx, and this will be the derivative of the original, implicitly defined function.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
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
FACEBOOK // https://www.facebook.com/KristaKingMath
TWITTER // https://twitter.com/KristaKingMath
INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King
Tagged under: Krista King,educational,calculus expert, ,implicit,expert,implicit differentiation,differentiation,calculus,derivatives
Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.
Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip
Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans
1. Students enter a simple code
2. You play the video
3. The students comment
4. You review and reflect
* Whiteboard required for teacher-paced activities
With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.
Carry out a quickfire formative assessment to see what the whole class is thinking
Create interactive presentations to spark creativity in class
Student teams can create and share collaborative presentations from linked devices
Turn any public video into a live chat with questions and quizzes