What is the tangent of 1/(sqrt(8x)) ?

The tangent of 1/(sqrt(8x)) is y=-1/(4sqrt(2)a_{0)^{3/2}}x+3/(4sqrt(2)\sqrt{a_{0)}}

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tangent of 1/(sqrt(8x))

tangent of

\frac{1}{8 x}

y = - \frac{1}{4 2 a _{0}^{\frac{3}{2}}} x + \frac{3}{4 2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{2 2 a _{0}})

Find the slope of

y = \frac{1}{8 x} : \frac{d y}{d x} = - \frac{1}{4 2 x ^{\frac{3}{2}}}

Compute the slope of

y = \frac{1}{8 x}

x = a_{0} : m = - \frac{1}{4 2 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{1}{4 2 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{1}{2 2 a _{0}}) : y = - \frac{1}{4 2 a _{0}^{\frac{3}{2}}} x + \frac{3}{4 2 a _{0}}

y = - \frac{1}{4 2 a _{0}^{\frac{3}{2}}} x + \frac{3}{4 2 a _{0}}

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\frac{d}{d x} (sin^{3} (3 x^{2} + 6 x))

\int_{0}^{3} (\frac{x}{3} + 5) d x

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

\frac{\partial}{\partial x} (\frac{1}{6} x^{3})

What is the tangent of 1/(sqrt(8x)) ?
The tangent of 1/(sqrt(8x)) is y=-1/(4sqrt(2)a_{0)^{3/2}}x+3/(4sqrt(2)\sqrt{a_{0)}}