Partial Derivatives of Multivariable Functions
Most curves are functions of one variable, but surfaces and other functions can involve many variables . For surfaces, you might express the y coordinate as a function of the x and z coordinates, as shown in Equation A.12.
| (A.12) y as a function of x and z. |  |
In many cases, you will need to compute the partial derivative , which is the derivative with respect to only one of the two variables. In a general math class, this can become a bit complicated. You can safely compute partial derivatives fairly easily for most of the applications in this book. When computing the partial derivative of a multivariable polynomial, choose which variable you want to find the derivative for and treat the others as constants. Then, compute the derivative as you did for simple polynomials . Repeat for all the variables as needed. Equation A.13 shows an example of this.
| (A.13) A more complicated partial derivative. |  |
This is not a general approach for all equations. I haven't given you enough information to solve Equation A.14 (and many others).
| (A.14) A more complicated multivariable polynomial. |  |
The examples in this book do not involve this kind of equation, and I want to stress the point that I am giving you only what you need in this book.
