# 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 andx2 + y2 = 16,find y '.

#### Example 2

 Find y ' given that y is a function of x and xy + x2 + y2 = 0.

#### Exercise 1

Use implicit differentiation to find y', assuming that y is a function of x.

• x3 + y3 = 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?

•  ey2x = y

#### Exercise 4

Using implicit differentiation, what is y ' in the following equation?

• xy2 + x3y = 4x

#### Exercise 5

What is y ' in the following equation?