Let f(x, y) = x^2 + 2 x y + y^2 + 3 x + 5 y. Find {partial f} / {partial x} (2, -3) and {partial...


Let {eq}f(x,\ y) = x^2 + 2 x y + y^2 + 3 x + 5 y {/eq}. Find {eq}\dfrac {\partial f} {\partial x} (2,\ -3) {/eq} and {eq}\dfrac {\partial f} {\partial y} (2,\ -3) {/eq}.

Partials Derivatives:

We can use the same general rules of differentiation to carry out the partial derivatives of a function of two or more variables, simply that when we differentiate with respect to one variable, the others are considered constants, the following formula being useful:

{eq}\displaystyle u =f(x,y,z)\\ \displaystyle du =\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz\\ {/eq}

Answer and Explanation: 1

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Given the function:

{eq}\displaystyle f(x,y)= x^2 +2xy+y^2+3x+5y \\ {/eq}

First we perform the derivative of the function with respect to...

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The Chain Rule for Partial Derivatives


Chapter 14 / Lesson 4

This lesson defines the chain rule. It goes on to explore the chain rule with partial derivatives and integrals of partial derivatives.

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