What is the tangent of y=(3sqrt(x)+x)(2-x^2) ?

The tangent of y=(3sqrt(x)+x)(2-x^2) is

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tangent of y=(3sqrt(x)+x)(2-x^2)

tangent of

y = (3 x + x) (2 - x^{2})

y = (- 3 a_{0}^{2} - 6 a_{0} a_{0} - \frac{3 a _{0}^{\frac{3}{2}}}{2} + \frac{3}{a _{0}} + 2) x + 2 a_{0}^{3} + 3 a_{0}^{2} a_{0} + 3 a_{0} + \frac{3 a _{0}^{\frac{5}{2}}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (3 a_{0} + a_{0}) (2 - a_{0}^{2}))

Find the slope of

y = (3 x + x) (2 - x^{2}) : \frac{d y}{d x} = - 3 x^{2} - 6 x x - \frac{3 x ^{\frac{3}{2}}}{2} + \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 = - 3 a_{0}^{2} - 6 a_{0} a_{0} - \frac{3 a _{0}^{\frac{3}{2}}}{2} + \frac{3}{a _{0}} + 2

Find the line with slope m=

- 3 a_{0}^{2} - 6 a_{0} a_{0} - \frac{3 a _{0}^{\frac{3}{2}}}{2} + \frac{3}{a _{0}} + 2

and passing through

(a_{0}, (3 a_{0} + a_{0}) (2 - a_{0}^{2})) : y = (- 3 a_{0}^{2} - 6 a_{0} a_{0} - \frac{3 a _{0}^{\frac{3}{2}}}{2} + \frac{3}{a _{0}} + 2) x + 2 a_{0}^{3} + 3 a_{0}^{2} a_{0} + 3 a_{0} + \frac{3 a _{0}^{\frac{5}{2}}}{2}

y = (- 3 a_{0}^{2} - 6 a_{0} a_{0} - \frac{3 a _{0}^{\frac{3}{2}}}{2} + \frac{3}{a _{0}} + 2) x + 2 a_{0}^{3} + 3 a_{0}^{2} a_{0} + 3 a_{0} + \frac{3 a _{0}^{\frac{5}{2}}}{2}

f (x) = \frac{x - 7}{- 5 x - 10}

\frac{d}{d x} (13 x^{2} - 5 x + 8)

7 y^{^{'}} + 1 y = 8 e^{3} x, y (0) = 9

f (x) = sin (3 x) cos (5 x)

\frac{1}{1 + 4 x}

What is the tangent of y=(3sqrt(x)+x)(2-x^2) ?
The tangent of y=(3sqrt(x)+x)(2-x^2) is