Version 6.2 Collection of 19 DHS DHS Ryabushko

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DHS - 6.2
Find y ´and y ".
№ 1.19. xy - 6 = cosy.
Find y ´and y ".
№ 2.19. {X = sin2t; y = cos²t.
№ 3.19. For a given function y and calculate the argument x0 ‴ y (x0); y = cos²x; x0 = π / 4.
№ 4.19. Write a formula for the derivative of n - th order for the function y = 10ˣ
№ 5.19. Find out at what point of the curve y = x³ / 3 - x² / 2 - 7x + 9; the tangent of the angle of the axis Ox - π / 4.
№ 6.19. The material point moves along the hyperbola xy = 20, so that its abscissa x uniformly increases with the speed of 1 m / s.
How fast changes ordinate when the point passes the position (4, 5)?