What is the tangent of sqrt(5x+6) ?

The tangent of sqrt(5x+6) is y= 5/(2sqrt(5a_{0)+6)}x+sqrt(5a_{0)+6}-(5a_{0})/(2sqrt(5a_{0)+6)}

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tangent of sqrt(5x+6)

tangent of

5 x + 6

y = \frac{5}{2 5 a _{0} + 6} x + 5 a_{0} + 6 - \frac{5 a _{0}}{2 5 a _{0} + 6}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0} + 6)

Find the slope of

y = 5 x + 6 : \frac{d y}{d x} = \frac{5}{2 5 x + 6}

Compute the slope of

y = 5 x + 6

x = a_{0} : m = \frac{5}{2 5 a _{0} + 6}

Find the line with slope m=

\frac{5}{2 5 a _{0} + 6}

and passing through

(a_{0}, 5 a_{0} + 6) : y = \frac{5}{2 5 a _{0} + 6} x + 5 a_{0} + 6 - \frac{5 a _{0}}{2 5 a _{0} + 6}

y = \frac{5}{2 5 a _{0} + 6} x + 5 a_{0} + 6 - \frac{5 a _{0}}{2 5 a _{0} + 6}

\frac{\partial}{\partial x} (- \frac{8 x - 4 y}{- 5 x - 9 y})

\frac{d}{d x} (\frac{2 x ^{5} - 15}{x ^{4}})

e^{6 y}

What is the tangent of sqrt(5x+6) ?
The tangent of sqrt(5x+6) is y= 5/(2sqrt(5a_{0)+6)}x+sqrt(5a_{0)+6}-(5a_{0})/(2sqrt(5a_{0)+6)}