What is implicit x=sec(1/y) ?

The answer to implicit x=sec(1/y) is (dy)/(dx)=-(y^2)/(sec(1/y)tan(1/y))

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implicit x=sec(1/y)

implicit derivative

x = sec (\frac{1}{y})

\frac{d y}{d x} = - \frac{y ^{2}}{sec ( \frac{1}{y} ) tan ( \frac{1}{y} )}

Solution steps

x = sec (\frac{1}{y})

Treat

y

y (x)

Differentiate both sides:

1 = - \frac{sec ( \frac{1}{y} ) tan ( \frac{1}{y} ) \frac{d y}{d x}}{y ^{2}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ^{2}}{sec ( \frac{1}{y} ) tan ( \frac{1}{y} )}

\frac{d y}{d x} = - \frac{y ^{2}}{sec ( \frac{1}{y} ) tan ( \frac{1}{y} )}

What is implicit x=sec(1/y) ?
The answer to implicit x=sec(1/y) is (dy)/(dx)=-(y^2)/(sec(1/y)tan(1/y))