Implicit Differentiation?
a. In your own words, state the guidelines for implicit differentiation.
b. Think about your explanation and use it to solve the following problem (with regards to your explanation):
#\(xy)^2+x^3y^2=3y#
a. In your own words, state the guidelines for implicit differentiation.
b. Think about your explanation and use it to solve the following problem (with regards to your explanation):
1 Answer
The derivative is:
Explanation:
a) Implicit Differentiation is used for an implicitly defined function (or relation). An implicitly defined function/relation is one that does not express
By contrast, explicit differentiation is used for an explicitly defined function or relation, that is one that has been "solved for
To use implicit differentiation, you find the derivative of the expression in terms of
b) For the given example, I would start with a bit of algebra to simplify the job:
We differentiate in terms of
We now collect all of the terms containing
Now we factor out