Lecture Note
University
Massachusetts Institute of TechnologyCourse
Multivariable CalculusPages
1
Academic year
2022
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Views
18
p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:23px;font-family:ArialMT;color:#000000;} Level curves and partial derivatives. Computing partial derivatives There is a notation used in physics and applied math that allows one to computethese things. So how to compute? In Mathematics, the same symbol may be used for both a variable and one of itsderivatives. For example, f(x) is the derivative of f(x), where y is treated as aconstant and x is treated as a variable.Furthermore, if we want to find partial derivatives with respect to y, we can simplydifferentiate the equation with respect to x. Let's consider the function f(x, y) = x3y + y2. Then we can take its partial derivativeswith respect to x and y. To find the derivative of a function that is raised to the thirdpower, you must take the derivative of each term and apply the multiplication rule.The derivative of x cubed is 3 times x squared times the constant plus 0, because ysquared is a constant. If you instead consider a partial derivative, then theexpression is a constant times y. The derivative of y is 1, so that's just x cubed. Thederivative of y squared is 2 y.
Partial Derivatives and Computing Techniques
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