Question

найти производную y = (ln (x^{2} + 2x + 3)^{sin^{3}x})

Answer 1

$(ln(x^{2}+2x+3)^{sin^{3}x})'=(sin^3x*ln(x^2+2x+3))'=(sin^3x)'ln(x^2+2x+3)+(ln(x^2+2x+3))'sin^3x=3sin^2x*(sinx)'ln(x^2+2x+3)+\frac{1}{x^2+2x+3}*(x^2+2x+3)'sin^3x=3sin^2x*cosx*ln(x^2+2x+3)+\frac{2x+2}{x^2+2x+3}*sin^3x$