f(x)可导,求y=[xf(x^2)]^2的导数.因为我做的答案跟辅导书上答案不同,求验证,

Question

f(x)可导,求y=[xf(x^2)]^2的导数.因为我做的答案跟辅导书上答案不同,求验证,

Answer 1

令t=x²,t'=2x
y=tf²(t)
y'=t'f²(t)+t[f²(t)]'
=t'f²(t)+t*2*f²(t)*[f(t)]'
=t'f²(t)+t*2*f²(t)*f'(t)*t'
=2xf²(x²)+2x²*f²(x²)*f'(x²)*2x
=2xf²(x²)+4x³*f²(x²)*f'(x²)