User:Egm6321.f11/WolframAlpha syntax

WolframAlpha (WA) expressions

I take some examples to illustrate the use of WA for symbolic computation. The examples are to explain in detail my lecture in [[media: 2010_10_28_14_54_20.djvu | PEA1 F10 p.31-2]].

1. For $$\displaystyle \frac{d^2}{dx^2} \frac{e^{rx}}{x}$$, use the following expression in WA:

You can use either square brackets [] or parentheses.

Even though the above expression without the brackets also works, it is recommended to keep the brackets for clarity.

2. For $$\displaystyle x \frac{d^2}{dx^2} \frac{e^{rx}}{x} - 2 \frac{d}{dx} \frac{e^{rx}}{x} $$, use the following expression in WA:

Note the square brackets [] surrounding the 2nd term; try to remove the square brackets, then you would get a completely different expression, which is the same as

The reason is because of the confusion in interpreting and

You can also bracket the first term; WA should work for you too, i,e.,

Alternatively, you can also use the "derivative" function:

3. For $$\displaystyle x \frac{d^2}{dx^2} \frac{e^{rx}}{x} - 2 \frac{d}{dx} \frac{e^{rx}}{x} + x \frac{e^{rx}}{x}$$, use the following expression in WA:

Again, note that I bracketed the 3rd term, but you actually don't need to do so, and WA still gives you the same result (you need to bracket ONLY the 2nd term; but bracket only the 1st term did not work).

WolframAlpha uses the syntax of Mathematica; for more details on the role of the square brackets, see FE1 S11 Team 7 HW6.7 Syntax of WolframAlpha.