Отыскать производную функции: 1) (3x^2-1/x^3) 2) (x/3+7)^6 ,3) e^x cos x

1) (3x^2 - 1/x^3) = (3x^2) - (1/x^3) = 2 * 3x - (-3/x) = 6x + 3/x^4;

2) [(x/3 + 7)^6] = 6 * (x/3 + 7)^5 * (x/3 + 7) = 6(x/3 + 7)^5 * [(x/3) + 7] = 6(x/3 + 7)^5 * 1/3 * x + 0  = 6(x/3 + 7)^5 * 1/3 * 1 = 2(x/3 + 7)^5 ;

3) (e^x * cosx) = e^x * (cosx) + (e^x) * cosx = e^x * (- sinx) + e^x * cosx = e^x * cosx - e^x * sinx = e^x * (cosx - sinx) = e^x(cosx - sinx);

4) (2^x/sinx) = [(2^x) * sinx - 2^x * (sinx)]/(sinx)^2 = [2^x * ln2sinx - 2^xcosx]/(sinx)^2 = 2^x(ln2sinx - cosx)/(sinx)^2.