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

The tangent of y=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 y=sqrt(5x+11)

tangent of

y = 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}

n = 2 \sum \infty \frac{e ^{n}}{n !}

\int \frac{3}{x ( x ^{4} + 4 )} d x

\frac{d}{d x} (x ln (\frac{x}{5}))

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

\frac{1}{2} bh

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