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Partial differentiation is used for finding maxima and minima in optimization problems. Let us discuss it in details.
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It is a derivative where we hold some independent variable as constant and find derivative with respect to another independent variable. For example, suppose we have an equation of a curve with X and Y coordinates in it as 2 independent variables. To find the slope in the direction of X, while keeping Y fixed, we will find the partial derivative. Similarly, we can find the slope in the direction of Y keeping X as Fixed. Partial differentiation builds with the use of concepts of ordinary differentiation.
So we should be familiar with the methods of doing ordinary first-order differentiation. Obviously, for a function of one variable, its partial derivative is the same as the ordinary derivative. Constants, when added to functions, will differentiate to 0 but constants multiplying the functions, are retained and so still multiply the derivative. Question Find the partial derivative of the following function in x and y with respect to x and y separately.
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Great job! Hopefully, now you understand a little more about multivariable functions and derivatives! Partial Derivatives Lab Introduction In this lesson, we'll get some more practice with partial derivatives. Unlock your future in tech.
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