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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:

With several possible answers.

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.

Thanks in advance.

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$$-\frac{e^{-x}}{\sqrt{e^{-2x}-1}} = -\frac{1}{e^x\sqrt{e^{-2x}-1}}$$

$$-\frac{1}{\sqrt{e^{2x}}\sqrt{e^{-2x}-1}}$$

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  • $\begingroup$ Sometimes you see a relatively simple solution and wonder how it went so easily over your head for so long! Thanks a bunch :) $\endgroup$ – MrMeowMeow Apr 20 at 16:31
  • $\begingroup$ Sure, no problem. Plz mark the answer as accepted if you have no further queries. $\endgroup$ – Vizag Apr 20 at 16:33

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