What is the tangent of y=6tan(x),\at x= pi/3 ?

The tangent of y=6tan(x),\at x= pi/3 is y=24x+6sqrt(3)-8pi

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tangent of y=6tan(x),\at x= pi/3

tangent of

y = 6 tan (x), at x = \frac{π}{3}

y = 24 x + 63 - 8 π

Solution steps

Find the tangent point:

(\frac{π}{3}, 63)

Find the slope of

y = 6 tan (x) : \frac{d y}{d x} = 6 sec^{2} (x)

Compute the slope of

y = 6 tan (x)

x = \frac{π}{3} : m = 24

Find the line with slope m=

24

and passing through

(\frac{π}{3}, 63) : y = 24 x + 63 - 8 π

y = 24 x + 63 - 8 π

\int \frac{10 x ^{2} - 9 x + 20}{x ^{3} + 4 x} d x

x y^{^{'}} + x y - y^{^{'}} - 2 y = 0

\int - 2 tan (2 x) d x

x^{2} y^{^{'}} + x y = 7

x \to 1 + lim (x^{2} + 2 x)

What is the tangent of y=6tan(x),\at x= pi/3 ?
The tangent of y=6tan(x),\at x= pi/3 is y=24x+6sqrt(3)-8pi