Skip to main content\(\newcommand{\deriv}[2]{\displaystyle \frac{d#1}{d#2}}
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Instructions.
Drag the slider for the angle to choose the unit vector
\(\mathbf u\text{,}\) and drag the slider for
\(s\) to move the point
\(P\) along the direction
\(\mathbf u\) starting at
\(P_0(1,1)\text{,}\) for the function
\(f(x,y) = 1 + x^2 + y^2\text{.}\) The readout compares the difference quotient
\(\big(f(P) - f(P_0)\big)/s\) with its limit as
\(s \to 0\text{,}\) which is the directional derivative
\(\left(D_{\mathbf u} f\right)_{P_0}\text{.}\)