en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of (x-6/x)^8

Solution

tangent of

(x - \frac{6}{x})^{8}

Solution

y = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}}) x - 7 a_{0}^{8} + 240 a_{0}^{6} - 3024 a_{0}^{4} + 12096 a_{0}^{2} - \frac{1306368}{a _{0}^{2}} + \frac{6531840}{a _{0}^{4}} - \frac{15676416}{a _{0}^{6}} + \frac{15116544}{a _{0}^{8}} + 90720

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (a_{0} - \frac{6}{a _{0}})^{8})

Find the slope of

y = (x - \frac{6}{x})^{8} : \frac{d y}{d x} = 8 (x - \frac{6}{x})^{7} (1 + \frac{6}{x ^{2}})

Compute the slope of

y = (x - \frac{6}{x})^{8}

at

x = a_{0} : m = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}})

Find the line with slope m=

8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}})

and passing through

(a_{0}, (a_{0} - \frac{6}{a _{0}})^{8}) : y = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}}) x - 7 a_{0}^{8} + 240 a_{0}^{6} - 3024 a_{0}^{4} + 12096 a_{0}^{2} - \frac{1306368}{a _{0}^{2}} + \frac{6531840}{a _{0}^{4}} - \frac{15676416}{a _{0}^{6}} + \frac{15116544}{a _{0}^{8}} + 90720

y = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}}) x - 7 a_{0}^{8} + 240 a_{0}^{6} - 3024 a_{0}^{4} + 12096 a_{0}^{2} - \frac{1306368}{a _{0}^{2}} + \frac{6531840}{a _{0}^{4}} - \frac{15676416}{a _{0}^{6}} + \frac{15116544}{a _{0}^{8}} + 90720

Popular Examples

derivative of (3x^2+4x+3/(x^2+1))

\frac{d}{d x} (\frac{3 x ^{2} + 4 x + 3}{x ^{2} + 1})

derivative of 2sec(x)+5cot(x)derivative of

2 sec (x) + 5 cot (x)

integral from 0 to pi of 2cos^2(x/2)

\int_{0}^{π} 2 cos^{2} (\frac{x}{2}) d x

(\partial)/(\partial y)(xyz)

\frac{\partial}{\partial y} (x yz)

y^{''}+5y^'+11y=33

y^{^{''}} + 5 y^{^{'}} + 11 y = 33

Frequently Asked Questions (FAQ)

What is the tangent of (x-6/x)^8 ?
The tangent of (x-6/x)^8 is