# 1314L23 - Lesson 23 Partial Derivatives When we are asked...

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1 Lesson 23 Partial Derivatives When we are asked to find the derivative of a function of a single variable, ), ( x f we know exactly what to do. However, when we have a function of two variables, there is some ambiguity. With a function of two variables, we can find the slope of the tangent line at a point P from an infinite number of directions. We will only consider two directions, either parallel to the x axis or parallel to the y axis. When we do this, we fix one of the variables. Then we can find the derivative with respect to the other variable. So, if we fix y , we can find the derivative of the function with respect to the variable x. And if we fix x , we can find the derivative of the function with respect to the variable y . These derivatives are called partial derivatives . First Partial Derivatives We will use two different notations: or x f x f consider y as a constant or y f y f consider x as a constant We can also evaluate a partial derivative at a given point. Example 1:

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1314L23 - Lesson 23 Partial Derivatives When we are asked...

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