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Section 13.7 : Directional Derivatives

2. Determine the gradient of the following function.

\[f\left( {x,y,z} \right) = x\cos \left( {xy} \right) + {z^2}{y^4} - 7xz\] Show Solution

Not really a lot to do for this problem. Here is the gradient.

\[\nabla f = \left\langle {{f_x},{f_y},{f_z}} \right\rangle = \require{bbox} \bbox[2pt,border:1px solid black]{{\left\langle {\cos \left( {xy} \right) - xy\sin \left( {xy} \right) - 7z, - {x^2}\sin \left( {xy} \right) + 4{z^2}{y^3},2z{y^4} - 7x} \right\rangle }}\]