Find the differential of y in the function: y=(x^3-2)^2 ?

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Answer 1 · 2018-04-09T10:41:36

To differentiate this function the function of a function rule can be used or the function can be expanded and differentiate.

The first way is as follows:

#y = (x^3-2)^2#
#y' = 2(x^3 - 2) xx 3x^2#

Therefore:
#y' = 6x^2(x^3 - 2)#

The second method is as follows:

#y = (x^3-2)^2#
#y = x^6 - 4x^3 - 4#
#y' = 6x^5 - 12x^2#

Therefore:
#y' = 6x^2(x^3 - 2)#