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