What is the tangent of sqrt(x+5) ?

The tangent of sqrt(x+5) is y= 1/(2sqrt(a_{0)+5)}x+sqrt(a_{0)+5}-(a_{0})/(2sqrt(a_{0)+5)}

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tangent of sqrt(x+5)

tangent of

x + 5

y = \frac{1}{2 a _{0} + 5} x + a_{0} + 5 - \frac{a _{0}}{2 a _{0} + 5}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + 5)

Find the slope of

y = x + 5 : \frac{d y}{d x} = \frac{1}{2 x + 5}

Compute the slope of

y = x + 5

x = a_{0} : m = \frac{1}{2 a _{0} + 5}

Find the line with slope m=

\frac{1}{2 a _{0} + 5}

and passing through

(a_{0}, a_{0} + 5) : y = \frac{1}{2 a _{0} + 5} x + a_{0} + 5 - \frac{a _{0}}{2 a _{0} + 5}

y = \frac{1}{2 a _{0} + 5} x + a_{0} + 5 - \frac{a _{0}}{2 a _{0} + 5}

\frac{d ^{4} y}{d x ^{4}} - 3 y = 0

y = x, y = ln (x), x = 1, x = 2

\frac{d}{d x} (\frac{1}{1 + 3 x})

\int_{1}^{e} ln (x^{2}) d x

\int_{110}^{160} \frac{160}{3 x ^{2}} d x

What is the tangent of sqrt(x+5) ?
The tangent of sqrt(x+5) is y= 1/(2sqrt(a_{0)+5)}x+sqrt(a_{0)+5}-(a_{0})/(2sqrt(a_{0)+5)}