Is it possible to define $x+x+x+x...x$ times?

Question

Is it possible to define $x+x+x+x...x $ times? I need to compute its derivative. It differs from the derivative of $x^2$. It evaluates to $x$ via sum of derivatives.

Answer 1

There are two problems with this expression.

• First: How would $\underbrace{x+x+...+x+x}_{x}$ make sense if $x$ is not an integer? How would you add 3.5 to it self 3.5 times?
• Second: This one is more related to calculus. Assume that $\underbrace{x+x+...+x+x}_{x}$ is well defined, then you don't only have to differentiate all the individual $x$es , but also the $x$ under the brace. However you can't really do that using this notation.

Just notate it with $x^2$ and find the correct derivative $2x$.