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

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

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tangent of 1/(sqrt(4x))

tangent of

\frac{1}{4 x}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = \frac{1}{4 x}

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

Find the line with slope m=

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

and passing through

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

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

\int_{4}^{9} \frac{x - x}{x} d x

\int 3 \cdot x + 4 d x

n = 0 \sum \infty \frac{4}{n ^{2}}

\frac{d y}{d x} 9 x^{2} y + 9 y^{2} x = - 9

\int e^{2 x - 2} d x

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