Question
Find $D_{\mathfrak{u}} f$ at $P$.$$\begin{array}{l}{f(x, y, z)=\sin x y z ; P\left(\frac{1}{2}, \frac{1}{3}, \pi\right)} \\ {\mathbf{u}=\frac{1}{\sqrt{3}} \mathbf{i}-\frac{1}{\sqrt{3}} \mathbf{j}+\frac{1}{\sqrt{3}} \mathbf{k}}\end{array}$$
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The gradient of a function is a vector that points in the direction of the greatest rate of increase of the function, and its magnitude is the rate of increase in that direction. The gradient is given by the vector of partial derivatives of the function with Show more…
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