Transcription of Partial Derivatives - Simon Fraser University
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Partial Derivatives - Simon Fraser University
ECON 331 multivariable CalculusPartial DerivativesSingle variable calculus is really just a special case of multivariable calculus . For thefunctiony=f(x), we assumed thatywas the endogenous variable,xwas the exogenousvariable and everything else was a parameter. For example, given the equationsy=a+bxory=axnwe automatically treateda,b,andnas constants and took the derivative of y with respectto x (dy/dx). However, what if we decided to treatxas a constant and take the derivativewith respect to one of the other variables? Nothing precludes us from doing this. Considerthe equationy=axwheredydx=aNow suppose wefind the derivative ofywith respect toa,but TREATxas the we just reversed the roles played byaandxin our Variable Case:letz=f(x, y),whichmeans zis a function ofxandy .Inthiscasezis the endoge-nous (dependent) variable and bothxandyare the exogenous (independent) variables.
Multivariable Calculus Partial Derivatives Single variable calculus is really just a ”special case” of multivariable calculus. For the function y = f(x), we assumed that y was the endogenous variable, x was the exogenous variable and everything else was a parameter. For example, given the equations y = a+bx or y = axn
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