How to find $u$ for $u$ substitution in $\frac{1}{x^2+4}$

Question

In the problem $$\frac{d}{dx} \frac{1}{x^2+4}$$ why is the $u$ for $u$ substitution equal to $\cfrac{x}{2}$?

Answer 1

The substitution may be helpful for beginners to convert the derivative to a more recognisable format for some as this substitution eliminates the constant term from the expression in the denominator.

After the substitution you will end up with the derivative of-

$$\frac{1}{8}\frac{1}{u^2+1}$$

Which is directly written as an example in many textbooks. Then you can undo the substitution to get the answer.