What is the tangent of y=5tan(x) ?

The tangent of y=5tan(x) is y=5sec^2(a_{0})x+5tan(a_{0})-5sec^2(a_{0})a_{0}

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tangent of y=5tan(x)

tangent of

y = 5 tan (x)

y = 5 sec^{2} (a_{0}) x + 5 tan (a_{0}) - 5 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}, 5 tan (a_{0}))

Find the slope of

y = 5 tan (x) : \frac{d y}{d x} = 5 sec^{2} (x)

Compute the slope of

y = 5 tan (x)

x = a_{0} : m = 5 sec^{2} (a_{0})

Find the line with slope m=

5 sec^{2} (a_{0})

and passing through

(a_{0}, 5 tan (a_{0})) : y = 5 sec^{2} (a_{0}) x + 5 tan (a_{0}) - 5 sec^{2} (a_{0}) a_{0}

y = 5 sec^{2} (a_{0}) x + 5 tan (a_{0}) - 5 sec^{2} (a_{0}) a_{0}

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\frac{\partial}{\partial x} (2 x \cdot sin (9 x^{2} y))

\int \frac{1}{25 x ^{2} + 1} d x

What is the tangent of y=5tan(x) ?
The tangent of y=5tan(x) is y=5sec^2(a_{0})x+5tan(a_{0})-5sec^2(a_{0})a_{0}