Version 6.2 Collection of 16 DHS DHS Ryabushko

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DHS - 6.2
Find y´and y".
№ 1.16. siny = 7x + 3y.
Find y´and y".
№ 2.16. {X = arcsin t; y = √ 1 - t².
№ 3.16. For a given function y and calculate the argument x0 ‴ y (x0); y = x cos2x; x0 = π / 12.
№ 4.16. Write a formula for the derivative of n - th order for the function y = exp (-5x);
№ 5.16. Write the equation of the tangent to the curve y = 4 sin6x; at the point with the abscissa x = π / 18.
№ 6.16. By moving the axis Ox two material points; laws of motion which x = 5t² - t + 6 and x = 4t² + 18. How fast these points away from each other at the time of the meeting?

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