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Home Differentiation Implicit Functions Examples Example 1
 
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Example 1

Given the equation x + xy = 2y, find dy/dx.

Step 1

02_differentiation-466.gif.

We find each side by the Sum and Product Rules,

02_differentiation-467.gif

Thus our new equation is

02_differentiation-468.gif

Step 2

 

Solve for dy/dx.

02_differentiation-469.gif

We can check our answer by solving the original equation for y and using ordinary differentiation:

02_differentiation-470.gif

By the Quotient Rule,

02_differentiation-471.gif

A third way to find dy/dx is to solve the original equation for x, find dx/dy, and then use the Inverse Function Rule.

02_differentiation-472.gif

To see that our three answers

02_differentiation-473.gif

are all the same we substitute 02_differentiation-474.gif for y:

02_differentiation-475.gif
Home Differentiation Implicit Functions Examples Example 1

Last Update: 2006-11-15