# How does $\frac{-e^{-x}}{\sqrt{e^{-2x}-1}}$ rearrange?

I have been revising for my engineering mathematics exam which has a multiple choice question in it, which asks the following:

The derivative of $$\arcsin(e^{-x})$$ equals:

I have managed to find the derivative as far as $$-\dfrac{e^{-x}}{\sqrt{e^{-2x}-1}}$$ but this is not a valid option in the paper. I consulted an online calculator which rearranged the answer to $$-\dfrac{1}{\sqrt{{e}^{2x}-1}}$$ which is a valid option but the calculator doesn't explain the steps and I'd like to understand how to rearrange my answer to this form.
$$-\frac{e^{-x}}{\sqrt{e^{-2x}-1}} = -\frac{1}{e^x\sqrt{e^{-2x}-1}}$$
$$-\frac{1}{\sqrt{e^{2x}}\sqrt{e^{-2x}-1}}$$