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

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

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tangent of x+sqrt(x)

tangent of

x + x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = x + x

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

Find the line with slope m=

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

and passing through

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

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

x \to a lim (f (x) (g (x)))

\frac{\partial}{\partial θ} (r (θ))

\frac{d}{d x} ((x^{2} - 2 x) e^{4 x})

\int (x + 1)^{- 8} d x

\frac{\partial}{\partial y} (x^{2} - 2 x y + y^{2})

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