What is the tangent of (4x-3)^{1/2} ?

The tangent of (4x-3)^{1/2} is y= 2/((4a_{0)-3)^{1/2}}x+(4a_{0}-3)^{1/2}-(2a_{0})/((4a_{0)-3)^{1/2}}

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tangent of (4x-3)^{1/2}

tangent of

(4 x - 3)^{\frac{1}{2}}

y = \frac{2}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}} x + (4 a_{0} - 3)^{\frac{1}{2}} - \frac{2 a _{0}}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (4 a_{0} - 3)^{\frac{1}{2}})

Find the slope of

y = (4 x - 3)^{\frac{1}{2}} : \frac{d y}{d x} = \frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}

Compute the slope of

y = (4 x - 3)^{\frac{1}{2}}

x = a_{0} : m = \frac{2}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}}

Find the line with slope m=

\frac{2}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}}

and passing through

(a_{0}, (4 a_{0} - 3)^{\frac{1}{2}}) : y = \frac{2}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}} x + (4 a_{0} - 3)^{\frac{1}{2}} - \frac{2 a _{0}}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}}

y = \frac{2}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}} x + (4 a_{0} - 3)^{\frac{1}{2}} - \frac{2 a _{0}}{( 4 a _{0} - 3 ) ^{\frac{1}{2}}}

x y^{^{'}} + y = 3 cos (x)

\frac{\partial}{\partial x} (\frac{6}{5} - \frac{6}{5} e^{- 20 x})

n = 2 \sum \infty \frac{3}{n \cdot ( n + 3 )}

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 7

\int (t^{2})^{2} + (t)^{2} d t

What is the tangent of (4x-3)^{1/2} ?
The tangent of (4x-3)^{1/2} is y= 2/((4a_{0)-3)^{1/2}}x+(4a_{0}-3)^{1/2}-(2a_{0})/((4a_{0)-3)^{1/2}}