What is the tangent of 12x^{1/2} ?

The tangent of 12x^{1/2} is y= 6/(a_{0)^{1/2}}x+6a_{0}^{1/2}

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tangent of 12x^{1/2}

tangent of

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

y = \frac{6}{a _{0}^{\frac{1}{2}}} x + 6 a_{0}^{\frac{1}{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 12 a_{0}^{\frac{1}{2}})

Find the slope of

y = 12 x^{\frac{1}{2}} : \frac{d y}{d x} = \frac{6}{x ^{\frac{1}{2}}}

Compute the slope of

y = 12 x^{\frac{1}{2}}

x = a_{0} : m = \frac{6}{a _{0}^{\frac{1}{2}}}

Find the line with slope m=

\frac{6}{a _{0}^{\frac{1}{2}}}

and passing through

(a_{0}, 12 a_{0}^{\frac{1}{2}}) : y = \frac{6}{a _{0}^{\frac{1}{2}}} x + 6 a_{0}^{\frac{1}{2}}

y = \frac{6}{a _{0}^{\frac{1}{2}}} x + 6 a_{0}^{\frac{1}{2}}

x \to a lim (2 x - 1)

- \frac{40 ( 9 + 5 x ^{2} )}{( 9 - 5 x ^{2} ) ^{2}}

\int_{1}^{4} 2 x 5 + x^{2} d x

\frac{\partial}{\partial x} (e^{a x^{3}})

y = sec (5 x)

What is the tangent of 12x^{1/2} ?
The tangent of 12x^{1/2} is y= 6/(a_{0)^{1/2}}x+6a_{0}^{1/2}