Option 15 DHS 6.2

Option 15 DHS 6.2

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