What is the tangent of y=x(27x^{-2}+4) ?

The tangent of y=x(27x^{-2}+4) is y=(-(27)/(a_{0)^2}+4)x+(54)/(a_{0)}

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tangent of y=x(27x^{-2}+4)

tangent of

y = x (27 x^{- 2} + 4)

y = (- \frac{27}{a _{0}^{2}} + 4) x + \frac{54}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} (\frac{27}{a _{0}^{2}} + 4))

Find the slope of

y = x (27 x^{- 2} + 4) : \frac{d y}{d x} = - \frac{27}{x ^{2}} + 4

Compute the slope of

y = x (27 x^{- 2} + 4)

x = a_{0} : m = - \frac{27}{a _{0}^{2}} + 4

Find the line with slope m=

- \frac{27}{a _{0}^{2}} + 4

and passing through

(a_{0}, a_{0} (\frac{27}{a _{0}^{2}} + 4)) : y = (- \frac{27}{a _{0}^{2}} + 4) x + \frac{54}{a _{0}}

y = (- \frac{27}{a _{0}^{2}} + 4) x + \frac{54}{a _{0}}

x \to + 2 + lim (\frac{x}{x - 2})

\int x \cdot e^{- s x} d x

\frac{\partial}{\partial y} (\frac{e ^{y}}{e ^{x} + e ^{y}})

\frac{d}{d x} (3 x^{2} - 2 x + 5)

\int (x y e^{x z}) d z

What is the tangent of y=x(27x^{-2}+4) ?
The tangent of y=x(27x^{-2}+4) is y=(-(27)/(a_{0)^2}+4)x+(54)/(a_{0)}