Question

大一高数题f'(x)=x+sinx,则df(x²)=?

Answer 1

由f'(x)=x+sinx

f(x)=∫(x+sinx)dx=(x²/2)-cosx+C

f(x²)=x^4/2-cos(x²)+C

df(x²)=[x^4/2-cos(x²)+C]'=2x^3+2xsin(x²)