Question

f(cosx)的导数=sinx,f(cosx)=多少?不是-cosx!

Answer 1

f(cosx)'=sinx=√(1-cos^2x)所以：f(x)'=√(1-x^2)y=∫√(1-x^2)dx=x√(1-x^2)-∫x*(1/2)*(-2x)/√(1-x^2)dx=x√(1-x^2)-∫(1-x^2-1)dx/√(1-x^2)=x√(1-x^2)-∫√(1-x^2)dx+∫dx/√(1-x^2)y=x√(1-x^2)-y+arcsinx+c...