What is the tangent of-3/(sqrt(x)) ?

The tangent of-3/(sqrt(x)) is y= 3/(2a_{0)^{3/2}}x-9/(2sqrt(a_{0))}

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tangent of-3/(sqrt(x))

tangent of

- \frac{3}{x}

y = \frac{3}{2 a _{0}^{\frac{3}{2}}} x - \frac{9}{2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = - \frac{3}{x}

x = a_{0} : m = \frac{3}{2 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

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

and passing through

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

y = \frac{3}{2 a _{0}^{\frac{3}{2}}} x - \frac{9}{2 a _{0}}

(arctan (cos (x)))^{^{'}}

y^{^{''}} - y^{^{'}} - 6 y = 20 e^{- 2 x}

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

2 y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} + 3 y = 0

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

What is the tangent of-3/(sqrt(x)) ?
The tangent of-3/(sqrt(x)) is y= 3/(2a_{0)^{3/2}}x-9/(2sqrt(a_{0))}