Find a formula for D^n_x(1/x).
(The n is superscript and the x is subscript)
To find a formula for the nth derivative of 1/x with respect to x, we can use the general power rule for derivatives.
Let's start by writing 1/x as x^(-1). Applying the power rule, we have:
d^n/dx(x^(-1)) = (-1)^n * n! / x^(n+1)
Therefore, the formula for D^n_x(1/x) is given by:
D^n_x(1/x) = (-1)^n * n! / x^(n+1)
Please note that this formula is valid for n being a non-negative integer and x being a non-zero real number.