What is the tangent of f(x)=(5x-1)^{-1/6},\at x=13 ?

The tangent of f(x)=(5x-1)^{-1/6},\at x=13 is y=-5/768 x+449/768

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tangent of f(x)=(5x-1)^{-1/6},\at x=13

tangent of

f (x) = (5 x - 1)^{- \frac{1}{6}}, at x = 13

y = - \frac{5}{768} x + \frac{449}{768}

Solution steps

Find the tangent point:

(13, \frac{1}{2})

Find the slope of

f (x) = (5 x - 1)^{- \frac{1}{6}} : \frac{df ( x )}{d x} = - \frac{5}{6 ( 5 x - 1 ) ^{\frac{7}{6}}}

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 = - \frac{5}{768}

Find the line with slope m=

- \frac{5}{768}

and passing through

(13, \frac{1}{2}) : y = - \frac{5}{768} x + \frac{449}{768}

y = - \frac{5}{768} x + \frac{449}{768}

x \to 0 + lim ((\frac{1}{x})^{3 x})

y = 2 x^{2} + x, (1, 2)

\int_{5}^{2} x d x

y^{^{'}} + 10 y = 10

\int \frac{x}{x ^{2} + 3 x + 9} d x

What is the tangent of f(x)=(5x-1)^{-1/6},\at x=13 ?
The tangent of f(x)=(5x-1)^{-1/6},\at x=13 is y=-5/768 x+449/768