![]() Therefore, \(∂f/∂x\) represents the slope of the tangent line passing through the point \((x,y,f(x,y))\) parallel to the \(x\)-axis and \(∂f/∂y\) represents the slope of the tangent line passing through the point \((x,y,f(x,y))\) parallel to the \(y\)-axis. If we choose to change \(y\) instead of \(x\) by the same incremental value \(h\), then the secant line is parallel to the \(y\)-axis and so is the tangent line. Thread: Multivariable calculus Introduction to double integrals Double integrals as iterated integrals Double integral examples Double integrals as volume. As \(h\) approaches zero, the slope of the secant line approaches the slope of the tangent line. ![]() ![]() ![]() Therefore, the slope of the secant line represents an average rate of change of the function \(f\) as we travel parallel to the \(x\)-axis. Multivariate Differential Calculus Starting Point: The Univariate Derivative Function Notation and Conceptual Foundations From Univariate to Multivariate. ![]()
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