What is the tangent of xsqrt(x) ?

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

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tangent of xsqrt(x)

tangent of

x x

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

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 = \frac{3 a _{0}}{2}

Find the line with slope m=

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

and passing through

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

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

\int \frac{16}{x ^{3} - 4 x ^{2}} d x

y \to - 2 lim (y^{3} (5 - 3 y^{2}))

y^{^{'}} = \frac{y}{x} + e^{- \frac{y}{x}}

\int_{0}^{2} k (2 - x)

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

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