# At a Glance - Using Leibniz Notation

Some things to remember for implicit differentiation:

• 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.

With these things in mind, we're ready to get cracking.

#### Example 1

 Find  given thatx2 + y2 = 4.

#### Example 2

 What is the derivative of y with respect to x given that4y2 + 8y = 2x2?

#### Example 3

 Assuming y is a function of x andxy + x = y,what is ?

#### Exercise 1

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

• 4y = x

#### Exercise 2

In the following equation what is the derivative of y with respect to x?

•  sin y = x2

#### Exercise 3

Find the derivative of y with respect to x in the following equation

•  ln (xy) = x + y

#### Exercise 4

Find in the following equation.

• y3 + x2yx = y

#### Exercise 5

What is in the following equation?