How do you find the derivative of #3(x^2-2)^4#?

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Answer 1 · 2015-06-04T13:17:24

We can use the chain rule, which states that #(dy)/(dx)=(dy)/(du)(du)/(dx)#.

To do so, we'll rename #u=x^2-2#, thus rewriting the expression as #y=3u^4#

Following chain rule's statements:

#(dy)/(du)=12u^3#
#(du)/(dx)=2x#

Combining them:

#(dy)/(dx)=12u^3(2x)#. Now, we need to substitute #u#.

#(dy)/(dx)=12(x^2-2)^3(2x)=color(green)(24x(x^2-2)^3)#