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

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

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tangent of y=x+sqrt(x)

tangent of

y = 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}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : 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 + y e^{(\frac{y}{x})}) d x - (x e^{\frac{y}{x}}) d y = 0

\frac{d y}{e ^{y}} = x d x

\int 6 x^{2} (x^{2} + 2) d x

x \to \infty lim (2 x + 1)

\int e^{- 2 x} cos (x) d x

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