What is the tangent of sqrt(3x+1) ?

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

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tangent of sqrt(3x+1)

tangent of

3 x + 1

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0} + 1)

Find the slope of

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

Compute the slope of

y = 3 x + 1

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

Find the line with slope m=

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

and passing through

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

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

\int \frac{1}{x ^{4} + x ^{2}} d x

x^{2} e^{\frac{1}{x}}

\frac{\partial}{\partial x} (t^{2} x - t)

\int \frac{x ^{2}}{x ^{4} - 20 x ^{2} - 125} d x

\frac{d}{d x} (5 \cdot 4^{x})

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