What is the tangent of (x^3-25x)^{12}(-5) ?

The tangent of (x^3-25x)^{12}(-5) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of (x^3-25x)^{12}(-5)

tangent of

(x^{3} - 25 x)^{12} (- 5)

y = - 60 (a_{0}^{3} - 25 a_{0})^{11} (3 a_{0}^{2} - 25) x + 175 a_{0}^{36} - 49500 a_{0}^{34} + 6393750 a_{0}^{32} - 498437500 a_{0}^{30} + 26103515625 a_{0}^{28} - 966796875000 a_{0}^{26} + 2.59424 E 13 a_{0}^{24} - 2 5^{7} \cdot 55440 a_{0}^{22} - 1.69189 E 14 a_{0}^{22} + 2 5^{8} \cdot 27225 a_{0}^{20} + 2 5^{7} \cdot 495000 a_{0}^{20} - 2 5^{9} \cdot 8800 a_{0}^{18} - 2 5^{8} \cdot 247500 a_{0}^{18} + 2 5^{10} \cdot 1650 a_{0}^{16} + 2 5^{9} \cdot 82500 a_{0}^{16} - 2 5^{11} \cdot 120 a_{0}^{14} - 2 5^{10} \cdot 16500 a_{0}^{14} + 2 5^{12} \cdot 55 a_{0}^{12}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - 5 (a_{0}^{3} - 25 a_{0})^{12})

Find the slope of

y = (x^{3} - 25 x)^{12} (- 5) : \frac{d y}{d x} = - 60 (x^{3} - 25 x)^{11} (3 x^{2} - 25)

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - 60 (a_{0}^{3} - 25 a_{0})^{11} (3 a_{0}^{2} - 25)

Find the line with slope m=

- 60 (a_{0}^{3} - 25 a_{0})^{11} (3 a_{0}^{2} - 25)

and passing through

(a_{0}, - 5 (a_{0}^{3} - 25 a_{0})^{12}) : y = - 60 (a_{0}^{3} - 25 a_{0})^{11} (3 a_{0}^{2} - 25) x + 175 a_{0}^{36} - 49500 a_{0}^{34} + 6393750 a_{0}^{32} - 498437500 a_{0}^{30} + 26103515625 a_{0}^{28} - 966796875000 a_{0}^{26} + 2.59424 E 13 a_{0}^{24} - 2 5^{7} \cdot 55440 a_{0}^{22} - 1.69189 E 14 a_{0}^{22} + 2 5^{8} \cdot 27225 a_{0}^{20} + 2 5^{7} \cdot 495000 a_{0}^{20} - 2 5^{9} \cdot 8800 a_{0}^{18} - 2 5^{8} \cdot 247500 a_{0}^{18} + 2 5^{10} \cdot 1650 a_{0}^{16} + 2 5^{9} \cdot 82500 a_{0}^{16} - 2 5^{11} \cdot 120 a_{0}^{14} - 2 5^{10} \cdot 16500 a_{0}^{14} + 2 5^{12} \cdot 55 a_{0}^{12}

y = - 60 (a_{0}^{3} - 25 a_{0})^{11} (3 a_{0}^{2} - 25) x + 175 a_{0}^{36} - 49500 a_{0}^{34} + 6393750 a_{0}^{32} - 498437500 a_{0}^{30} + 26103515625 a_{0}^{28} - 966796875000 a_{0}^{26} + 2.59424 E 13 a_{0}^{24} - 2 5^{7} \cdot 55440 a_{0}^{22} - 1.69189 E 14 a_{0}^{22} + 2 5^{8} \cdot 27225 a_{0}^{20} + 2 5^{7} \cdot 495000 a_{0}^{20} - 2 5^{9} \cdot 8800 a_{0}^{18} - 2 5^{8} \cdot 247500 a_{0}^{18} + 2 5^{10} \cdot 1650 a_{0}^{16} + 2 5^{9} \cdot 82500 a_{0}^{16} - 2 5^{11} \cdot 120 a_{0}^{14} - 2 5^{10} \cdot 16500 a_{0}^{14} + 2 5^{12} \cdot 55 a_{0}^{12}

What is the tangent of (x^3-25x)^{12}(-5) ?
The tangent of (x^3-25x)^{12}(-5) is