Question

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

Answer 1

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

Answer 2

I can't get past this

Answer 3

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

Answer 4

that's why you have to rewrite and use implicit differentiation

\[y=\sec^{-1} \left( \frac{ 1 }{ t } \right)\Rightarrow \sec y = \frac{ 1 }{ t }\]

\[d(\sec y )= d \left( \frac{ 1 }{ t } \right) \Rightarrow (\sec y)( \tan y)\frac{ dy }{ dt }=-\frac{ 1 }{ t^2 } \Rightarrow \frac{ dy }{ dt }=-\frac{ 1 }{ t^2 } \cdot \frac{ 1 }{ (\sec y)( \tan y) }\]