How do you differentiate #y = cos^-1 (e^-t)#?

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How do you differentiate #y = cos^-1 (e^-t)#?

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Answer 1 · 2015-08-29T16:57:29

Differentiate implicitly.

Explanation:

#y=cos^-1 (e^(–t))#
#cos y = e^(–t)#

Differentiating wrt #t#:
#–sin y dy/dt = –e^(–t)#
#–sqrt(1-cos^2 y) dy/dt = –e^(–t)#
#–sqrt(1-e^(–2t)) dy/dt = –e^(–t)#
#dy/dt = e^(–t) / sqrt(1-e^(–2t))#

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How do you differentiate #y = cos^-1 (e^-t)#?

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