Question

производная от f(x)=sin2x/x^1/2

Answer 1

$f(x)=\frac{sin2x}{x^{\frac{1}{2}}}\\f'(x)=\frac{(sin2x)'x^{\frac{1}{2}}-(x^{\frac{1}{2}})'sin2x}{(x^{\frac{1}{2}})^{2}}\\f'(x)=\frac{2cos2x*x^{\frac{1}{2}}-\frac{1}{2}x^{-\frac{1}{2}}sin2x}{x}\\f'(x)=\frac{4cos2x*x-sin2x}{2x^{\frac{3}{2}}}$