What is the tangent of sqrt(x-4) ?

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

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tangent of sqrt(x-4)

tangent of

x - 4

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = x - 4

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

Find the line with slope m=

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

and passing through

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

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

\frac{d}{d x} (e^{x^{y}})

\frac{d}{d x} (e^{x^{2}} sin (x^{3} - 2))

\frac{d}{d x} (x (x + 1))

\frac{d}{d x} (8^{x - 5})

\frac{d}{d x} (x (x^{2} - 1)^{2})

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