Ryabushko A.P. IDZ 6.2 option 15

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DHS - 6.2
Find y ´and y ".
№ 1.15. 4sin² (x + y) = x.
Find y ´and y ".
№ 2.15. {X = arctg t; y = Ln (1 + t²).
№ 3.15. For a given function y and calculate the argument x0 ‴ y (x0); y = x sin2x; x0 = - π / 4.
№ 4.15. Write a formula for the derivative of n - th order for the function y = 5ˣ;
№ 5.15. Write the equation of the normal to the curve y = 6 tg 5x; at the point with the abscissa x = π / 20.
№ 6.15. By moving the axis Ox two material points, the laws of motion that x = 3t² - 8 and y = 2t² + 5t + 6. How fast these points are removed from each other at the time of the meeting?