What is the tangent of x-x^3 ?

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

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tangent of x-x^3

tangent of

x - x^{3}

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

Compute the slope of

y = x - x^{3}

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{d}{d x} (\frac{x}{( 1 + x )})

\int \frac{x ^{2} + 3 x + 2}{x ^{2} ( x + 3 )} d x

\int \frac{a ^{t}}{t} d t

\int 6 sin^{3} (x) cos^{5} (x) d x

(x^{x})^{^{'}}