What is the tangent of 7/(sqrt(x)) ?

The tangent of 7/(sqrt(x)) is y=-7/(2a_{0)^{3/2}}x+(21)/(2sqrt(a_{0))}

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tangent of 7/(sqrt(x))

tangent of

\frac{7}{x}

y = - \frac{7}{2 a _{0}^{\frac{3}{2}}} x + \frac{21}{2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{7}{a _{0}})

Find the slope of

y = \frac{7}{x} : \frac{d y}{d x} = - \frac{7}{2 x ^{\frac{3}{2}}}

Compute the slope of

y = \frac{7}{x}

x = a_{0} : m = - \frac{7}{2 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{7}{2 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{7}{a _{0}}) : y = - \frac{7}{2 a _{0}^{\frac{3}{2}}} x + \frac{21}{2 a _{0}}

y = - \frac{7}{2 a _{0}^{\frac{3}{2}}} x + \frac{21}{2 a _{0}}

\int \frac{1}{- x ^{2} + 4 x - 1} d x

y = x^{2} - 12 x + 4

\int e^{t} sin (3 t) d t

2 tan^{2} (4 x)

\frac{\partial}{\partial x} (x^{2} y)

What is the tangent of 7/(sqrt(x)) ?
The tangent of 7/(sqrt(x)) is y=-7/(2a_{0)^{3/2}}x+(21)/(2sqrt(a_{0))}