What is the tangent of 2x+3/x ?

The tangent of 2x+3/x is y=(2-3/(a_{0)^2})x+6/(a_{0)}

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tangent of 2x+3/x

tangent of

2 x + \frac{3}{x}

y = (2 - \frac{3}{a _{0}^{2}}) x + \frac{6}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0} + \frac{3}{a _{0}})

Find the slope of

y = 2 x + \frac{3}{x} : \frac{d y}{d x} = 2 - \frac{3}{x ^{2}}

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 = 2 - \frac{3}{a _{0}^{2}}

Find the line with slope m=

2 - \frac{3}{a _{0}^{2}}

and passing through

(a_{0}, 2 a_{0} + \frac{3}{a _{0}}) : y = (2 - \frac{3}{a _{0}^{2}}) x + \frac{6}{a _{0}}

y = (2 - \frac{3}{a _{0}^{2}}) x + \frac{6}{a _{0}}

\int_{0}^{4} ∣ x - 3 ∣ d x

f (x) = \frac{4 x ^{2} + 4 x + 6}{x}

\int \frac{x ^{3} + x ^{2} + x + 3}{x ^{4} + 4 x ^{2} + 3} d x

\frac{d}{d x} ((x^{2} + 8)^{5})

\int (1 - x) (2 + x^{3}) d x

What is the tangent of 2x+3/x ?
The tangent of 2x+3/x is y=(2-3/(a_{0)^2})x+6/(a_{0)}