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

## Question:

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}