Question

设f′(cos x)=(sin x)的平方,且f(0)=0,求f(x)

Answer 1

记t=cos x 则(sin x)^2=1-t^2

即f'(t)=1-t^2,f(t)=-1/3t^3+t+c,由f(0)=0,c=0

所以f(x)=-1/3x^3+x ,x∈[-1,1]