Question

大一高数题f'(x)=x+sinx,则df(x²)=？

因为我头脑迟钝所以我希望好心人人帮我把解题步骤写的很详细

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)

Answer 2

d(f(x^2))=f'(x^2)*(x^2)'dx
=(x^2+sin(x^2))*2xdx
=(2x^3+2xsin(x^2))dx