If I am doing an implicit differentiation in a curve in R^2 for example, because I want to get the tangent line on a certain point... How am I suposed to know if I should differentiate it in terms of Y, or in terms of X?

mangicele4s

mangicele4s

Answered question

2022-09-22

If I am doing an implicit differentiation in a curve in R 2 for example, because I want to get the tangent line on a certain point... How am I suposed to know if I should differentiate it in terms of Y, or in terms of X?
Am I going to get two slopes, one that's perpendicular to the other one by changing the term that I am doing that differentiation? If so, how can I guarantee that the term choosed to differentiate will give me the slope for the tangent?!

Answer & Explanation

skarvama

skarvama

Beginner2022-09-23Added 5 answers

This is an excellent question, and it may be worth looking up the implicit function theorem for a full answer, i.e. when can you actually solve for an explicit function of y or of x given some implicit function f ( x , y ) = 0.
However, in general in Calculus, you have a function of the form y ( x ) implicitly defined. Meaning you have some curve in R 2 of the form f ( x , y ) = c, but you care about solving for the rate of change of y which depends on the variable x, which you take to be independent.
odenut6b

odenut6b

Beginner2022-09-24Added 3 answers

Thanks

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