Question

求y＝f²(x²)的导数

Answer 1

该函数属于复合函数，则令x²=u，则y=f²(u)=f(u)f(u)

则y的导数y'=f'(u)f(u)u'+f(u)f'(u)u'=2u'f'(u)f(u)=2*(2x)f'(x²)f(x²)=4xf'(x²)f(x²)

参考资料：

1.复合函数求导：网页链接

追问

可答案是4xf'(x²)f²(x²)啊

追答

估计是你参考书的答案错了，我这个是正确的。下面那个的回答答案也是这个

Answer 2

y=[f(x^2)]^2
y'
= 2f(x^2) . d/dx f(x^2)
= 2f(x^2) . f'(x^2) . d/dx (x^2)
= 2f(x^2) . f'(x^2) . (2x)
=4x.f(x^2).f'(x^2)

Answer 3

Answer 4