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You can differentiate a function when it only contains one changing variable, like f(x) = x2. It's derivative is f'(x) = 2x.

If a function contains more than one variable, like f(x,y) = x2 + y2, you can't just "find the derivative" generically because that doesn't specify what variable to take the derivative with respect to. Instead, you might "take the derivative with respect to x (treating y as a constant)" and get fx(x,y) = 2x or "take the derivative with respect to y (treating x as a constant)" and get fy(x,y) = 2y.

This is a partial derivative--when you take the derivative of a function with many variable with respect to one of the variables while treating the rest as constants.

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โˆ™ 2012-08-12 20:42:53
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Q: What is the difference between the differentiation of the function and the partial differentiation of the function?
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