已知y=a•cos2(1/x2),求y´.
y=a•cos2(1/x2)可以看成由y=au2,u=cosυ,υ=1/x2三个函数复合而成的函数,由复合函数求导法则,得到dy/dx=dy/du•du/dυ•dυ/dx=(2au)•(-sinυ)•[-(2/x3)]=[2a•cos(1/x2)]•[-sin(1/x2)]•[-(2/x3)]=2a/x3•sin(2/x2)
已知y=a•cos2(1/x2),求y´.
y=a•cos2(1/x2)可以看成由y=au2,u=cosυ,υ=1/x2三个函数复合而成的函数,由复合函数求导法则,得到dy/dx=dy/du•du/dυ•dυ/dx=(2au)•(-sinυ)•[-(2/x3)]=[2a•cos(1/x2)]•[-sin(1/x2)]•[-(2/x3)]=2a/x3•sin(2/x2)