What is the tangent of 12(x-1/x)^2,\at x=2 ?

The tangent of 12(x-1/x)^2,\at x=2 is y=45x-63

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tangent of 12(x-1/x)^2,\at x=2

tangent of

12 (x - \frac{1}{x})^{2}, at x = 2

y = 45 x - 63

Solution steps

Find the tangent point:

(2, 27)

Find the slope of

y = 12 (x - \frac{1}{x})^{2} : \frac{d y}{d x} = 12 (2 x - \frac{2}{x ^{3}})

Compute the slope of

y = 12 (x - \frac{1}{x})^{2}

x = 2 : m = 45

Find the line with slope m=

45

and passing through

(2, 27) : y = 45 x - 63

y = 45 x - 63

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

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

x^{4} - 8 x^{2} + 16

x^{2} + 2 x

\int \frac{1}{9 e ^{- 2 x} - 1} d x

What is the tangent of 12(x-1/x)^2,\at x=2 ?
The tangent of 12(x-1/x)^2,\at x=2 is y=45x-63