$\frac{n}{x}$

Base Case: $\frac{n}{x}$

Note :

–           The technical definition involves the absolute value . However, this is not always emphasized, and at times you may see your teacher drop the absolute value bars .

–           You will also see these problems include a domain (i.e., x>0). Usually, this domain is given so that you do not have to use the absolute value bars , and does not have value beyond that.

–           This rule only applies if the power on your x is 1. If it is anything other than 1, then it is an algebraic rewrite.

–           They sometimes like to be tricky with this special case and will write the problem with the x portion not in the denominator, but rather in the top of the fraction raised to the negative 1 ^st power , -1 .

Ex: $f‘\left(x\right)=n{x}^{–1}$

This is the same as $\frac{n}{x^1}$. This is just undoing one of your standard rewrites, x’s on the Bottom of a Fraction.

Ex:  $n{x}^{–1}=\frac{n}{x^1}$

–           As soon as the problem is more than just your basic x , the problem’s primary method becomes a u-substitution .