What is the tangent of 4sqrt(x) ?

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

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tangent of 4sqrt(x)

tangent of

4 x

y = \frac{2}{a _{0}} x + 2 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0})

Find the slope of

y = 4 x : \frac{d y}{d x} = \frac{2}{x}

Compute the slope of

y = 4 x

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

Find the line with slope m=

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

and passing through

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

y = \frac{2}{a _{0}} x + 2 a_{0}

\frac{\partial}{\partial x} (y^{\frac{4}{x}})

0 \to 0 lim (ln (0))

x \to - \infty lim (\frac{4 - 7 x}{2 + 3 x})

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

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