What is the tangent of y=8(x-1/x)^4,\at x=2 ?

The tangent of y=8(x-1/x)^4,\at x=2 is y=135x-459/2

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tangent of y=8(x-1/x)^4,\at x=2

tangent of

y = 8 (x - \frac{1}{x})^{4}, at x = 2

y = 135 x - \frac{459}{2}

Solution steps

Find the tangent point:

(2, \frac{81}{2})

Find the slope of

y = 8 (x - \frac{1}{x})^{4} : \frac{d y}{d x} = 32 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

Compute the slope of

y = 8 (x - \frac{1}{x})^{4}

x = 2 : m = 135

Find the line with slope m=

135

and passing through

(2, \frac{81}{2}) : y = 135 x - \frac{459}{2}

y = 135 x - \frac{459}{2}

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

x \to 0 lim (\frac{6 e ^{x} - 6}{x})

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

\frac{d}{d x} (cos (4 x) + sin (4 x))

10 y^{^{''}} + 1000 y = 0

What is the tangent of y=8(x-1/x)^4,\at x=2 ?
The tangent of y=8(x-1/x)^4,\at x=2 is y=135x-459/2