Question
The Laplacian of a function $f(x, y)$ is defined by $\nabla^{2} f(x, y)=f_{x x}(x, y)+f_{y y}(x, y) .$ Compute $\nabla^{2} f(x, y)$ for $f(x, y)=x^{3}-2 x y+y^{2}$
Step 1
This is denoted as $f_{xx}(x, y)$. The first derivative of $f(x, y)$ with respect to $x$ is $3x^{2}-2y$. Differentiating this again with respect to $x$ gives us $f_{xx}(x, y) = 6x$. Show more…
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