Question

一道关于求导的高数题

求指点，还有这两问有什么区别，要怎么理解呢

Answer 1

Answer 2

f(x) =arcsinx
φ(x) = x^2
To find : d/dφ(x) [ f(φ(x)) ] and ( f[φ(x)])'
solution
f(φ(x)) = arcsin(x^2)
d/dφ(x) [ f(φ(x)) ]
=d/dφ(x) [ arcsin(x^2) ]
=d/dx [ arcsin(x^2) ] / d/dx[ φ(x)]
=d/dx [ arcsin(x^2) ] / (2x)
=[1/(2x)] . [2x/√(1 -x^4) ]
= 1/√(1 -x^4)
//
( f[φ(x)])'
=d/dx [ arcsin(x^2) ]
=2x/√(1 -x^4)