Use the quotient rule to derive the given equation. (Simplify your answers completely.)—(cot(x)) = −csc²(x)dxda (cot(x))dx=||ddxcos(x)-1|(−sin(x)) -cos²(x)(cos(x))

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Answered: Use the quotient rule to derive the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Tell if the function f(x) = −2 sin (10x)−4 is increasing, constant, or decreasing at x = −(1/2) and at x = (1/2).
A rescued whale is released into the ocean 400 meters due east of a coast guard station. The whale swims directly away from the shore. coast guard station point of release O tan(0) (a) Which of the following equations can be used to relate the angle, 0, and the distance between the whale and the point of release, x? O cos(0) O sec(0) = O sin(0) = O tan(0) = X 400 X 400 X 400 O cos² (0)- X 400 400 X O sec² (8) de dt de dt (b) Which of the following would be an appropriate related rate equation for the answer to part (a)? 1 dx 400 dt = O sec² (0) dx dt O sec(0)tan(0)- O cos²(e) de dt = = 8 1 dx 400 dt de 1 dx dt 400 dt = dx dt X whale 1 de 400 dt (c) If the whale swims at a constant rate of 60 meters per minute, how fast is the angle changing when the whale is 300 meters from the point of release? Give an exact answer. radians per minute
Verify the formula by differentiation. sec2 (9x + 5)dx = 1. tan (9x + 5) + C 6. Which function should be differentiated? O A. sec2(9x + 5) 1. O B. tan (9x + 5) + C 6.

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Use the quotient rule to derive the given equation. (Simplify your answers completely.) -(cot(x)) = -csc²(x) d (cot(x)) d dx d dx cos(x) -1 (-sin(x)) - - cos²(x) (cos(x))