What is the tangent of tan(x) ?

The tangent of tan(x) is y=sec^2(a_{0})x+tan(a_{0})-sec^2(a_{0})a_{0}

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tangent of tan(x)

tangent of

tan (x)

y = sec^{2} (a_{0}) x + tan (a_{0}) - sec^{2} (a_{0}) a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, tan (a_{0}))

Find the slope of

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

Compute the slope of

y = tan (x)

x = a_{0} : m = sec^{2} (a_{0})

Find the line with slope m=

sec^{2} (a_{0})

and passing through

(a_{0}, tan (a_{0})) : y = sec^{2} (a_{0}) x + tan (a_{0}) - sec^{2} (a_{0}) a_{0}

y = sec^{2} (a_{0}) x + tan (a_{0}) - sec^{2} (a_{0}) a_{0}

\frac{d}{d x} (10 x e^{- x})

\frac{d y}{d x} = \frac{2 x ^{3}}{y ^{2}}

\frac{d y}{d t} + 2 y = e^{\frac{t}{3}}

\int 17 tan^{2} (x) sec^{3} (x) d x

\frac{d}{d x} (\frac{1 + sec ( x )}{1 - sec ( x )})

What is the tangent of tan(x) ?
The tangent of tan(x) is y=sec^2(a_{0})x+tan(a_{0})-sec^2(a_{0})a_{0}