What is the tangent of sqrt(x+3) ?

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

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tangent of sqrt(x+3)

tangent of

x + 3

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + 3)

Find the slope of

y = x + 3 : \frac{d y}{d x} = \frac{1}{2 x + 3}

Compute the slope of

y = x + 3

x = a_{0} : m = \frac{1}{2 a _{0} + 3}

Find the line with slope m=

\frac{1}{2 a _{0} + 3}

and passing through

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

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

\int_{- 1}^{- 4} \frac{1 - x ^{4}}{x ^{2}} d x

\frac{1}{x}

\frac{x}{1 - x}

\frac{d e}{d x}

\frac{d}{d x} (\frac{3 x ^{2} - 12}{8 x})

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