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partial derivatives - Partial Derivatives – MADE EASY...

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Unformatted text preview: Partial Derivatives – MADE EASY! sources: http://mathworld.wolfram.com/PartialDerivative.html & http://en.wikipedia.org/wiki/Partial_derivative According to Wikipedia, the source of all knowledge on the internet, a partial derivative “of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).” Whoa!!! What did that say? I . Let’s look at a regular/total derivative dx dA where . 2 ) ( x x A ⋅ = π ( ) x x dx d dx dA ⋅ ⋅ = ⋅ = π π 2 2 . Simple enough, right? II . So what’s the deal with partial derivatives? Let’s find out… Let h r V ⋅ ⋅ = 2 3 1 π . Now the partial derivative of V with respect to r, r V ∂ ∂ , is done much the same way as dx dA , so we will look at dr dV . Consider the case where h is known, say h = 17.34 cm. Then h is considered a constant just like π was. Substitute this value in to get a better picture:...
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