Отыскать производную функций:1) 2x^6y^3-ln7y*ln8x=02) y=(5x^2+6)^arctg8x

1) 2xy - ln7y*ln8x=0;

(2xy - ln7y*ln8x)'=0;

12xy + 2x3yy' - (1/7y)7y'ln8x - ln7y(1/8x)8 = 0;

12xy + 6xyy' - (y'ln8x)/y - ln7y(1/x) = 0;

12xy + y'(6xy - (ln8x)/y) - ln7y(1/x) = 0;

y'(6xy - (ln8x)/y) = ln7y/x - 12xy;

y' = (ln7y/x - 12xy)/(6xy - (ln8x)/y).

2) y=(5x+6)^arctg8x;

lny = arctg8xln(5x+6);

(lny)' = (arctg8xln(5x+6))';

y'/y = (8/(1+64x))ln(5x+6) + (10xarctg8x)/(5x+6);

y' = y((8/(1+64x))ln(5x+6) + (10xarctg8x)/(5x+6));

y' = ((5x^2+6)^arctg8x)((8/(1+64x))ln(5x+6) + (10xarctg8x)/(5x+6));