Question

Найдите производную функции y= x^ sin x

Answer 1

$y=x^{\sin x} = e^{\ln x^{\sin x}}= e^{\sin x \cdot \ln x}\\ y' = (e^{\sin x \cdot \ln x})' = e^{\sin x \cdot \ln x} \cdot (\sin x \cdot \ln x)'= e^{\sin x \cdot \ln x} \cdot (\cos x \ln x +\frac{\sin x}{x}) =\\ = x^{\sin x} \cdot (\cos x \ln x +\frac{\sin x}{x})$

Answer 2

y'=sinx*x^(sinx-1) * sinx ' = sinx *(x^sinx)/x *cosx= sinxcosx * (x^sinx)/x