What is the tangent of sec(x) ?

The tangent of sec(x) is y=sec(a_{0})tan(a_{0})x+sec(a_{0})-sec(a_{0})tan(a_{0})a_{0}

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tangent of sec(x)

tangent of

sec (x)

y = sec (a_{0}) tan (a_{0}) x + sec (a_{0}) - sec (a_{0}) tan (a_{0}) a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, sec (a_{0}))

Find the slope of

y = sec (x) : \frac{d y}{d x} = sec (x) tan (x)

Compute the slope of

y = sec (x)

x = a_{0} : m = sec (a_{0}) tan (a_{0})

Find the line with slope m=

sec (a_{0}) tan (a_{0})

and passing through

(a_{0}, sec (a_{0})) : y = sec (a_{0}) tan (a_{0}) x + sec (a_{0}) - sec (a_{0}) tan (a_{0}) a_{0}

y = sec (a_{0}) tan (a_{0}) x + sec (a_{0}) - sec (a_{0}) tan (a_{0}) a_{0}

x \to 0 lim (arctan (x))

\frac{s - 1}{s ^{2} - 2 s + 1}

\frac{\partial}{\partial y} (ln (x + 6 y + 5 z))

\int \frac{10}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

x \to 8 - lim (\frac{x - 8}{∣ x - 8 ∣})

What is the tangent of sec(x) ?
The tangent of sec(x) is y=sec(a_{0})tan(a_{0})x+sec(a_{0})-sec(a_{0})tan(a_{0})a_{0}