How do you find the derivative of(x^5+x^6-8)^3?

1 Answer
Lucy
Jul 18, 2018

Below

Explanation:

#y=(x^5+x^6-8)^3#

Let #u=x^5+x^6-8#
then #(du)/(dx)=5x^4+6x^5#

Since #u=x^5+x^6-8#, then
#y=u^3#
#(dy)/(du)=3u^2#

Therefore,
#(dy)/(dx)=(dy)/(du)times(du)/(dx)#
=#3u^2times(5x^4+6x^5)#
=#3(x^5+x^6-8)^2(5x^4+6x^5)#

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