Question

найти производную функции и упростить ее
y=(2-x^2)cosx+2xsinx

Answer 1

$(x^n)'=nx^{n-1} \ (sin x)'=cos \ (cos x)'=-sin x \ (f(x)+g(x))'=f'(x)+g'(x) \ (f(g(x)))'=f'(g(x))cdot g'(x)$

$y=(2-x^2)cos x+2xsin x \ y'=(2-x^2)'cos x+(2-x^2)(cos x)'+2(x'sin x+x(sin x)')= \ =-2xcos x-(2-x^2)sin x+2(sin x+xcos x)= \ =-2xcos x-2sin x+x^2sin x+2sin x+2xcos x=x^2sin x$