At a Glance - Using Lagrange Notation
Not a fan of Leibniz notation? We can do implicit differentiation with Lagrange notation just as well.
Things to remember for implicit differentiation with Lagrange notation:
- x' = 1.
- since y is a function of x, any derivative involving y must use the chain rule.
- since y is a function of x, taking the derivative of xy (or of any other product involving both x and y) requires the product rule.
- since y is a function of x, taking the derivative of (or any other quotient involving both x and y) requires the quotient rule.
Example 1
If y is a function of x and x^{2} + y^{2} = 16, find y '. |
Example 2
Find y ' given that y is a function of x and xy + x^{2} + y^{2} = 0. |
Exercise 1
Use implicit differentiation to find y', assuming that y is a function of x.
- x^{3} + y^{3} = 4x
Exercise 2
Use implicit differentiation to find y', assuming that y is a function of x.
- y = cos(y) + 2x
Exercise 3
What is y' in the following equation?
- e^{y2} – x = y
Exercise 4
Using implicit differentiation, what is y ' in the following equation?
- xy^{2} + x^{3}y = 4x
Exercise 5
What is y ' in the following equation?