What is the tangent of y=xsqrt(x) ?

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

tangent of y=xsqrt(x)

tangent of

y = 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}

y^{^{''}} - (\frac{2}{x}) y^{^{'}} - (\frac{7}{x ^{2}}) y = 0

\frac{d}{d x} (ln (sec (x^{2})))

\int e^{x + y^{2}} d x

\int y 10 + 10 y - 25 y^{2} d y

x \to 0 lim (\frac{ln ( 1 + 3 x )}{x})

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