What is the tangent of (x^3-16x)^8 ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of (x^3-16x)^8

tangent of

(x^{3} - 16 x)^{8}

y = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16) x - 23 a_{0}^{24} + 2688 a_{0}^{22} - 136192 a_{0}^{20} + 3899392 a_{0}^{18} - 68812800 a_{0}^{16} + 763363328 a_{0}^{14} - 5167382528 a_{0}^{12} + 19327352832 a_{0}^{10} + 1 6^{8} a_{0}^{8} - 34359738368 a_{0}^{8}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (a_{0}^{3} - 16 a_{0})^{8})

Find the slope of

y = (x^{3} - 16 x)^{8} : \frac{d y}{d x} = 8 (x^{3} - 16 x)^{7} (3 x^{2} - 16)

Compute the slope of

y = (x^{3} - 16 x)^{8}

x = a_{0} : m = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16)

Find the line with slope m=

8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16)

and passing through

(a_{0}, (a_{0}^{3} - 16 a_{0})^{8}) : y = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16) x - 23 a_{0}^{24} + 2688 a_{0}^{22} - 136192 a_{0}^{20} + 3899392 a_{0}^{18} - 68812800 a_{0}^{16} + 763363328 a_{0}^{14} - 5167382528 a_{0}^{12} + 19327352832 a_{0}^{10} + 1 6^{8} a_{0}^{8} - 34359738368 a_{0}^{8}

y = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16) x - 23 a_{0}^{24} + 2688 a_{0}^{22} - 136192 a_{0}^{20} + 3899392 a_{0}^{18} - 68812800 a_{0}^{16} + 763363328 a_{0}^{14} - 5167382528 a_{0}^{12} + 19327352832 a_{0}^{10} + 1 6^{8} a_{0}^{8} - 34359738368 a_{0}^{8}

\frac{\partial}{\partial y} (2 x^{4} y + 4)

\frac{d}{d x} (sec (0))

\int (4 - x^{2})^{\frac{1}{2}} d x

\frac{d y}{d t} = - \frac{3}{4 t}

\frac{\partial}{\partial x} (- \frac{2 x}{3 y})