Question

ПОМОГИТЕ ! СРОЧНО !......

Answer 1

$1)f(x)=2-frac{2}{sqrt{x} }=2-2x^{-frac{1}{2} }\\f'(x)=2'-2(x^{-frac{1}{2} })'=-2*(-frac{1}{2}x^{-frac{3}{2} })=frac{1}{sqrt{x^{3} } } =frac{1}{xsqrt{x} } \\2)f(x)=3-frac{1}{Sin^{2}x } =3-Sin^{-2} x\\f'(x)=3'-(Sin^{-2}x)'=2Sin^{-3}x*(Sinx)'=2Sin^{-3}x*Cosx=frac{2Cosx}{Sin^{3} x}$

$3)f(x)=frac{x^{3}-1 }{x^{2} } \\f'(x)=frac{(x^{3}-1)'*x^{2}-(x^{3}-1)*(x^{2})'}{(x^{2})^{2}}=frac{3x^{2}*x^{2}-(x^{3}-1)*2x   }{x^{4} }=frac{3x^{4}-2x^{4}+2x  }{x^{4} }=frac{x^{4}+2x }{x^{4} }=frac{x^{3} +2}{x^{3} }$