Question

Найдите производную функцию:
1) f(x)=cosx(1+sinx)
2) f(x)=x^3*tgx

Answer 1

$1) f'(x)=(cos x(1+sin x))'=cos' x(1+sin x)+cos x(1+sin x )'=\\=-sin x(1+sin x)+cos xbulletcos x=-sin x (1+sin x)+cos^2x;\\2) f'(x)=(x^3tgx)'=(x^3)'tgx+x^3(tgx)'=3x^2tgx+x^3bulletfrac{1}{cos^2x}=\\=3x^2tgx+frac{x^3}{cos^2x}=x^2(3tgx+frac{x}{cos^2x}).$