a) f(x, y) = xy \ln(3 + y), Find \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y},...


a) {eq}f(x, y) = xy \ln(3 + y),\ \mathrm{Find}\ \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial^2 f}{\partial x^2} {/eq} and {eq}\frac{\partial^2 f}{\partial y \partial x} {/eq}.

b) {eq}f(x, y) = \frac{e^{2xy}}{x + 1} {/eq}, Find {eq}f_x, f_y, f_{yy}\ \mathrm{and}\ f_{yx} {/eq}.

Partial Derivative:

The partial derivative is the way to find the derivative of a function of several variables with respect to one of those variables while other variables are kept constant.

First-order partial derivatives: {eq}f_{x}(x,y),f_{y}(x,y) {/eq}

Second-order partial derivatives: {eq}f_{xx}(x,y),f_{yy}(x,y),f_{xy}(x,y),f_{yx}(x,y) {/eq}

Answer and Explanation: 1

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{eq}f(x, y) = xy \ln(3 + y) {/eq}

We have to find {eq}\dfrac{\partial f}{\partial x}, \dfrac{\partial f}{\partial y}, \dfrac{\partial^2...

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Partial Derivative: Definition, Rules & Examples


Chapter 18 / Lesson 12

What is a Partial Derivative? Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.

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