What is the tangent of x^2+9x ?

The tangent of x^2+9x is y=(2a_{0}+9)x-a_{0}^2

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tangent of x^2+9x

tangent of

x^{2} + 9 x

y = (2 a_{0} + 9) x - a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} + 9 a_{0})

Find the slope of

y = x^{2} + 9 x : \frac{d y}{d x} = 2 x + 9

Compute the slope of

y = x^{2} + 9 x

x = a_{0} : m = 2 a_{0} + 9

Find the line with slope m=

2 a_{0} + 9

and passing through

(a_{0}, a_{0}^{2} + 9 a_{0}) : y = (2 a_{0} + 9) x - a_{0}^{2}

y = (2 a_{0} + 9) x - a_{0}^{2}

\int (x - x^{3})^{2} d x

y = (6 x^{2} - 12 x + 12) e^{- 8 x}

\frac{d ^{2}}{d x ^{2}} (x^{2} + 1)

2 x^{2} + 3 x - 4

\frac{d}{d x} (ln (π x))