# Question About Derivative Operator's Usage

Very simple question, I didn't understand the way we are using derivative operator(dy/dx) when we want to derive multiple times such as $$d^{10}f(x)/dx^{10}$$ for a function such as;

$$f(x)=x^{12}-4x^{3}-4$$

Okey I get it when I want to derive a function 10 times I use $$d^{10}f(x)$$ but why I am using $$dx^{10}$$ at the bottom of the operator instead of $$d^{10}x$$ because I am not deriving for ''$$x^{10}$$'' variable but for just ''$$x$$'' variable for the each ''$$x$$'' in my function not for each ''$$x^{10}$$'' I would love to hear an explanation about usage of this because it was so quick and basic in my lesson and I feel like this is important where I put these exponential expressions in the derivative operators.

## 1 Answer

This is just a matter of notation. You should read $$\left(\frac{d}{dx}\right)^{10}=\frac{d^{10}}{(dx)^{10}}$$ and this is usually written as $$\frac{d^{10}}{dx^{10}}$$, avoiding the parenthesis in the denominator.

• Oh now I get it thank you very much sir. – E.Berk Feb 26 at 9:06