What is the tangent of y= 5/(sqrt(x)) ?

The tangent of y= 5/(sqrt(x)) is y=-5/(2a_{0)^{3/2}}x+(15)/(2sqrt(a_{0))}

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tangent of y= 5/(sqrt(x))

tangent of

y = \frac{5}{x}

y = - \frac{5}{2 a _{0}^{\frac{3}{2}}} x + \frac{15}{2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{5}{a _{0}})

Find the slope of

y = \frac{5}{x} : \frac{d y}{d x} = - \frac{5}{2 x ^{\frac{3}{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 = - \frac{5}{2 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{5}{2 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{5}{a _{0}}) : y = - \frac{5}{2 a _{0}^{\frac{3}{2}}} x + \frac{15}{2 a _{0}}

y = - \frac{5}{2 a _{0}^{\frac{3}{2}}} x + \frac{15}{2 a _{0}}

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

x^{2} - 16 ln (x^{2})

\int 8 x e^{7 x} d x

\int sin (w x + \frac{π}{3}) sin (w x) d x

\frac{\partial}{\partial y} (\frac{ln ( x y )}{y})

What is the tangent of y= 5/(sqrt(x)) ?
The tangent of y= 5/(sqrt(x)) is y=-5/(2a_{0)^{3/2}}x+(15)/(2sqrt(a_{0))}