AP Calculus Classes near Dubai International Academic City

During a discussion with one of my students who was staying near Dubai International Academic City, I was asked why implicit differentiation is different from the usual derivative questions. While he knew the fundamentals, he was confused when x and y were both used in the same equation.

Dubai International Academic City is one of the significant higher education districts in the vicinity of Dubai Silicon Oasis and other emerging residential communities. The surrounding area naturally has a strong academic character.

Tutors.ae powered by Amourion teaches implicit differentiation, not by using the memorised notation, but by making the relationship of y with x visible in the student's thought.

Why do we need to do implicit differentiation?

Dr Anil Khare: If the equation relating x and y is not easily solved for y, then implicit differentiation is required. D/dx is used because y is presumed to be a function of x and when a function depends on y, one has to use the chain rule when taking the derivative.

What is the most frequently made implicit differentiation mistake?

Dr Anil Khare: The common implicit differentiation error is to differentiate y without considering its dependence on x as an independent constant or variable.

Is it possible to find the slope of tangents using implicit differentiation?

Dr Anil Khare: If you can get the differentiated equation of the implicit one, then solve it for dy/dx, then, at the given point, you can find the slope of the tangent.

How do students determine if a derivative is implicit?

Dr Anil Khare: To check an implicit derivative, each term involving y should be checked for the correct treatment of the chain rule and the algebra performed to isolate dy/dx.

Learn Implicit differentiation as a logical extension of the derivative rules, not as a special formula to be memorised, with tutors.ae.