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

The tangent of f(x)=6tan(x),\at x= pi/6 is y=8x+2sqrt(3)-(4pi)/3

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

tangent of

f (x) = 6 tan (x), at x = \frac{π}{6}

y = 8 x + 23 - \frac{4 π}{3}

Solution steps

Find the tangent point:

(\frac{π}{6}, 23)

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 8

Find the line with slope m=

8

and passing through

(\frac{π}{6}, 23) : y = 8 x + 23 - \frac{4 π}{3}

y = 8 x + 23 - \frac{4 π}{3}

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

\int (1 + tan (θ))^{5} sec^{2} (θ) d θ

\frac{d y}{d x} = \frac{y ( 2 x ^{3} - y ^{3} )}{x ( 2 x ^{3} - 3 y ^{3} )}

\frac{d}{d x} (\frac{2 x}{3})

\int 1 + (\frac{x ^{4} - 1}{2 x ^{2}})^{2} d x

What is the tangent of f(x)=6tan(x),\at x= pi/6 ?
The tangent of f(x)=6tan(x),\at x= pi/6 is y=8x+2sqrt(3)-(4pi)/3