I was doing a derivative problem for calculus.
The problem reads: $y=(\sec{x}+\tan{x})^5$ find $y'$.
I have found a derivative, I believe is almost certainly correct as I have checked it with a derivative calculator and done it many times.
My result is:
$$5(\tan{x}+\sec{x})^4(\sec{x}\tan{x}+\sec^2{x})$$
I have multiplied the parts together yet for some reason am having trouble getting to the right answer which according to the book is
$5\sec{x}(\sec{x} + \tan{x})^5$
I was wondering how the derivative I found could be simplified down to the correct answer. Unless somebody sees a glaring error with my derivative but like I said I have checked it with many sources. Thank you for your help.