What is the tangent of y=x-x^3(1) ?

The tangent of y=x-x^3(1) is y=(1-3a_{0}^2)x+2a_{0}^3

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tangent of y=x-x^3(1)

tangent of

y = x - x^{3} (1)

y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = x - x^{3} 1 : \frac{d y}{d x} = 1 - 3 x^{2}

Compute the slope of

y = x - x^{3} 1

x = a_{0} : m = 1 - 3 a_{0}^{2}

Find the line with slope m=

1 - 3 a_{0}^{2}

and passing through

(a_{0}, a_{0} - a_{0}^{3}) : y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

\frac{5}{s ^{2} + 4}

\frac{\partial}{\partial x} (- 4 x^{5} y^{- 5})

\frac{\partial}{\partial y} (1 + x y^{2})

\frac{d}{d x} (ln (x^{11}))

\frac{\partial}{\partial x} (x^{2} y^{3} (6 - x - y))

What is the tangent of y=x-x^3(1) ?
The tangent of y=x-x^3(1) is y=(1-3a_{0}^2)x+2a_{0}^3