What is the difference between a cation and an anion?

A cation is an element with a positive charge whereas an anion is an element with a negative charge. A cation has at least one more proton than electron. And an anion has at least one more electron than protons. Protons have positive charges and electrons have negative charges. Whichever you have more of determines the charge of the element. One trick to remember this is that cations are positive a because people like cats and see them as a positive thing. Anions however are negative and because onions make people cry people see them as negative.

What makes an element a noble gas?

Noble gasses have 8 valence electrons. This means that their outermost electron shell is full. The easiest way to identify a noble gas is to look at the periodic table. The noble gasses are in the far right column also called a group. Noble gasses are inert because of the fact that their outermost electron shell is full. It means the have just as many electrons as they need so they aren't looking to pick up new electrons or to get rid of any. They are content just the way they are and therefore are nonreactive.

How do I take the derivative of 4x^6?

To take the derivative of a function, you look at the variable, in this case x, to see what power it is to. In this case x is to the 6th power. x^n where n = 6. To take the derivative you multiply the original value (4x^6) by the power of x which is 6. You also subtract one from the power. It now looks like 6 * 4 x ^ (6 - 1) This can be simplified to 24 x ^ 5