What is the tangent of sqrt(5x+4) ?

The tangent of sqrt(5x+4) is y= 5/(2sqrt(5a_{0)+4)}x+sqrt(5a_{0)+4}-(5a_{0})/(2sqrt(5a_{0)+4)}

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tangent of sqrt(5x+4)

tangent of

5 x + 4

y = \frac{5}{2 5 a _{0} + 4} x + 5 a_{0} + 4 - \frac{5 a _{0}}{2 5 a _{0} + 4}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0} + 4)

Find the slope of

y = 5 x + 4 : \frac{d y}{d x} = \frac{5}{2 5 x + 4}

Compute the slope of

y = 5 x + 4

x = a_{0} : m = \frac{5}{2 5 a _{0} + 4}

Find the line with slope m=

\frac{5}{2 5 a _{0} + 4}

and passing through

(a_{0}, 5 a_{0} + 4) : y = \frac{5}{2 5 a _{0} + 4} x + 5 a_{0} + 4 - \frac{5 a _{0}}{2 5 a _{0} + 4}

y = \frac{5}{2 5 a _{0} + 4} x + 5 a_{0} + 4 - \frac{5 a _{0}}{2 5 a _{0} + 4}

\int \frac{sin ( 2 x )}{2 + cos ( x )} d x

\int_{- 5}^{5} \frac{y}{25 - y ^{2}} d y

x^{3} (2 x - 1)^{7}

x \to 0 lim (x + 2)

1 + x

What is the tangent of sqrt(5x+4) ?
The tangent of sqrt(5x+4) is y= 5/(2sqrt(5a_{0)+4)}x+sqrt(5a_{0)+4}-(5a_{0})/(2sqrt(5a_{0)+4)}