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Section 2-7 : Directional Derivatives

1. Determine the gradient of the following function.

\[f\left( {x,y} \right) = {x^2}\sec \left( {3x} \right) - \frac{{{x^2}}}{{{y^3}}}\] Show Solution

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

\[\nabla f = \left\langle {{f_x},{f_y}} \right\rangle = \require{bbox} \bbox[2pt,border:1px solid black]{{\left\langle {2x\sec \left( {3x} \right) + 3{x^2}\sec \left( {3x} \right)\tan \left( {3x} \right) - \frac{{2x}}{{{y^3}}},\frac{{3{x^2}}}{{{y^4}}}} \right\rangle }}\]