Solve x^a=partialx^a/partialx^bx^b

$$x ^ { a } = \frac { \partial x ^ { a } } { \partial x ^ { b } } x ^ { b }$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

$$∂\neq 0\text{ and }\left(b=0\text{ or }x\neq 0\right)$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b\in \mathrm{C}\text{, }&∂\neq 0\text{ and }x\neq 0\\b=0\text{, }&∂\neq 0\end{matrix}\right.$$

Solve for a

$$a\in \mathrm{R}$$

$$\left(x<0\text{ and }Denominator(a)\text{bmod}2=1\text{ and }∂\neq 0\text{ and }Denominator(b)\text{bmod}2=1\right)\text{ or }\left(∂\neq 0\text{ and }x>0\right)$$