How do you differentiate $y = {cos}^{- 1} (e^{- t})$ $y = cos^-1 (e^-t)$ ?

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How do you differentiate $y = {cos}^{- 1} (e^{- t})$ $y = cos^-1 (e^-t)$ ?

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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 $y = {cos}^{- 1} (e^{- t})$ $y = cos^-1 (e^-t)$ ?

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How do you differentiate $y = {cos}^{- 1} (e^{- t})$ $y = cos^-1 (e^-t)$ ?