What is the tangent of f^9 ?

The tangent of f^9 is y=9a_{0}^8f-8a_{0}^9

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tangent of f^9

tangent of

f^{9}

y = 9 a_{0}^{8} f - 8 a_{0}^{9}

Solution steps

Compute the tangent line to the general point

f = a_{0}

Find the tangent point:

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

Find the slope of

y = f^{9} : \frac{d y}{df} = 9 f^{8}

Compute the slope of

y = f^{9}

f = a_{0} : m = 9 a_{0}^{8}

Find the line with slope m=

9 a_{0}^{8}

and passing through

(a_{0}, a_{0}^{9}) : y = 9 a_{0}^{8} f - 8 a_{0}^{9}

y = 9 a_{0}^{8} f - 8 a_{0}^{9}

\frac{d y}{d x} = \frac{( 2 x + 1 )}{3 y}

\frac{d y}{d x} = 2 y - 4 x

f (x) = x^{2} (6 x + 1)^{3}

\int \frac{3}{x ^{- 1} + 1} d x

6 + 5 x