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OpenStudy (littlebird):

Derivative of y=sec^-1(1/t)

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OpenStudy (anonymous):

so sec y = (1/t) use implicit differentiation and then find dy/dx.

OpenStudy (littlebird):

I can't get past this

OpenStudy (anonymous):

it's not (sec (1/t))^-1 it's arcsec (1/t).

OpenStudy (anonymous):

that's why you have to rewrite and use implicit differentiation \[y=\sec^{-1} \left( \frac{ 1 }{ t } \right)\Rightarrow \sec y = \frac{ 1 }{ t }\] \[d(\sec y )= d \left( \frac{ 1 }{ t } \right) \Rightarrow (\sec y)( \tan y)\frac{ dy }{ dt }=-\frac{ 1 }{ t^2 } \Rightarrow \frac{ dy }{ dt }=-\frac{ 1 }{ t^2 } \cdot \frac{ 1 }{ (\sec y)( \tan y) }\]

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