I have been trying to find an analytical expression for the following:

$\frac{\partial {X^{+}}}{\partial {X}}$

In my case, $X$ has a constant rank.
I've found the formula for differentiating a pseudoinverse in [Golub's paper](http://i.stanford.edu/pub/cstr/reports/cs/tr/72/261/CS-TR-72-261.pdf) (equation 4.12): 

$$
\frac{\mathrm d}{\mathrm d x} A^+(x) =
 -A^+ \left( \frac{\mathrm d}{\mathrm d x} A \right) A^+
+A^+ A{^+}^T  \left( \frac{\mathrm d}{\mathrm d x} A^T \right) (1-A A^+)
+ (1-A^+ A) \left( \frac{\mathrm d}{\mathrm d x} A^T \right) A{^+}^T A^+
$$

but I can't see how to input the original matrix.