Question
Find the directional derivative of the function at thegiven point in the direction of the vector $v .$$$f(x, y)=\frac{x}{x^{2}+y^{2}}, \quad(1,2), \quad \mathbf{v}=\langle 3,5\rangle$$
Step 1
We use the quotient rule for differentiation to do this. For the partial derivative with respect to x, we have: \[ \frac{\partial f}{\partial x} = \frac{(x^2+y^2)(1) - (2x)(x)}{(x^2+y^2)^2} = \frac{y^2}{(x^2+y^2)^2} \] For the partial derivative with respect to Show more…
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