What is the tangent of 4/(x^2)-1/(sqrt(x)) ?

The tangent of 4/(x^2)-1/(sqrt(x)) is

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tangent of 4/(x^2)-1/(sqrt(x))

tangent of

\frac{4}{x ^{2}} - \frac{1}{x}

y = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}} x + \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}} - \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{7}{2}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}})

Find the slope of

y = \frac{4}{x ^{2}} - \frac{1}{x} : \frac{d y}{d x} = \frac{- 16 x ^{\frac{3}{2}} + x ^{3}}{2 x ^{\frac{9}{2}}}

Compute the slope of

y = \frac{4}{x ^{2}} - \frac{1}{x}

x = a_{0} : m = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}}

Find the line with slope m=

\frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}}

and passing through

(a_{0}, \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}}) : y = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}} x + \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}} - \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{7}{2}}}

y = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}} x + \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}} - \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{7}{2}}}

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

\int 2 y arctan (x) d y

y^{^{''}} - 2 y^{^{'}} - 24 y = 0, y (0) = - 1, y^{^{'}} (0) = 14

\int \frac{( x ^{3} )}{( x ^{4} + 5 )} d x

\int \frac{6}{sec ( 2 x ) - 1} d x

What is the tangent of 4/(x^2)-1/(sqrt(x)) ?
The tangent of 4/(x^2)-1/(sqrt(x)) is