What is the tangent of sqrt(5x+11) ?

The tangent of sqrt(5x+11) is y= 5/(2sqrt(5a_{0)+11)}x+sqrt(5a_{0)+11}-(5a_{0})/(2sqrt(5a_{0)+11)}

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tangent of sqrt(5x+11)

tangent of

5 x + 11

y = \frac{5}{2 5 a _{0} + 11} x + 5 a_{0} + 11 - \frac{5 a _{0}}{2 5 a _{0} + 11}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0} + 11)

Find the slope of

y = 5 x + 11 : \frac{d y}{d x} = \frac{5}{2 5 x + 11}

Compute the slope of

y = 5 x + 11

x = a_{0} : m = \frac{5}{2 5 a _{0} + 11}

Find the line with slope m=

\frac{5}{2 5 a _{0} + 11}

and passing through

(a_{0}, 5 a_{0} + 11) : y = \frac{5}{2 5 a _{0} + 11} x + 5 a_{0} + 11 - \frac{5 a _{0}}{2 5 a _{0} + 11}

y = \frac{5}{2 5 a _{0} + 11} x + 5 a_{0} + 11 - \frac{5 a _{0}}{2 5 a _{0} + 11}

f (x) = x^{2} + 5 x - 2

y = - x^{2} + x + 6, y = 4

\frac{3}{x - 3}

\int \frac{1}{r ^{2} - 2 r - 3} d r

\int_{2}^{x} sin (t^{4}) d t

What is the tangent of sqrt(5x+11) ?
The tangent of sqrt(5x+11) is y= 5/(2sqrt(5a_{0)+11)}x+sqrt(5a_{0)+11}-(5a_{0})/(2sqrt(5a_{0)+11)}