How do you find the derivative of #y = arccos(e^(5x))#?

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How do you find the derivative of #y = arccos(e^(5x))#?

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Answer 1 · 2016-04-10T09:55:44

#(-5e^(5x))/sqrt(1-e^10x), x<=0#.

Explanation:

#cos y=e^(5x)#.
#(-sin y) y'=5e^(5x)#.
#y'=-(5e^(5x))/(1-cos^2y#
#=.-(5e^(5x))/(1-e^(10x)#
Note that if x>0, #e^(5x)>1#, cos y > 1 and y becomes unreal.

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How do you find the derivative of #y = arccos(e^(5x))#?

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