Find the derivative of the function y = l n cos 3x 6. Find the largest and smallest value of the function

| September 3, 2021 | education

Find the derivative of the function y = l n cos 3x 6. Find the largest and smallest value of the function y = on the segment [3; 4] 7. Find the indefinite integral l n x dx 8. Calculate the area of the figure bounded by the lines y = 2x – x and y = 0 9. Find a particular solution of the differential equation y = – at x = 3; y = 4 10. Investigate the convergence of the series

f (x) ‘= ((2ln x + 3) ^ (- 1))’ = (2ln x + 3) ‘* ((2ln x + 3) ^ (- 1))’ = ((2ln x) ‘ + (3) ‘) * ((2ln x + 3) ^ (- 1))’ = (2 * (1 / x) + 0) * (-1) * (2ln x + 3) ^ (- 1 – 1) = (2 / x) * (-1) * (2ln x + 3) ^ (- 2) = (-2) / (x * (2ln x + 3) ^ 2).

f (x) ‘= (x ^ 3 * tg (x))’ = (x ^ 3) ‘* tg (x) + (x ^ 3) * (tg (x))’ = 3 * x ^ (3 – 1) * tan (x) + (x ^ 3) * (1 / (cos ^ 2 (x))) = 3x ^ 2 * tan (x) + (x ^ 3 / (cos ^ 2 (x)) ).

y ‘(3π / 4) = 3 * cos (3 * (3π / 4)) + 3 * sin (3 * (3π / 4)) = 3 * cos (9π / 4) + 3 * sin (9π / 4 ) = 3 * cos (2π + (π / 4)) + 3 * sin (2π + (π / 4)) = 3 * cos (π / 4) + 3 * sin (π / 4) = 3 * (cos (π / 4) + sin (π / 4)) = 3 * ((√2 / 2) + (√2 / 2)) = 3 * √2 = 3√2.

y ‘= (cos (arcsin x))’ = (arcsin x) ‘* (cos (arcsin x))’ = (1 / √ (1 – x ^ 2)) * (-sin (arcsin x)) = ( -sin (arcsin x)) / √ (1 – x ^ 2).



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