What is the tangent of 12(x-1/x)^4,\at x=2 ?

The tangent of 12(x-1/x)^4,\at x=2 is y= 405/2 x-1377/4

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tangent of 12(x-1/x)^4,\at x=2

tangent of

12 (x - \frac{1}{x})^{4}, at x = 2

y = \frac{405}{2} x - \frac{1377}{4}

Solution steps

Find the tangent point:

(2, \frac{243}{4})

Find the slope of

y = 12 (x - \frac{1}{x})^{4} : \frac{d y}{d x} = 48 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

Compute the slope of

y = 12 (x - \frac{1}{x})^{4}

x = 2 : m = \frac{405}{2}

Find the line with slope m=

\frac{405}{2}

and passing through

(2, \frac{243}{4}) : y = \frac{405}{2} x - \frac{1377}{4}

y = \frac{405}{2} x - \frac{1377}{4}

\frac{d}{d x} (5 + 4 x - x^{3})

x^{2} - 1, - 1, 6

y = (5 x^{4} - 3 x^{3}) (3 x^{2} - 7 x^{3})

\int \frac{3 z ^{2}}{y} d y

- 5 x^{3} - 1

What is the tangent of 12(x-1/x)^4,\at x=2 ?
The tangent of 12(x-1/x)^4,\at x=2 is y= 405/2 x-1377/4