How do you find the derivative of #y=(3x^5 - 4x^3 + 2)^23# using the chain rule?

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Answer 1 · 2015-12-24T22:24:03

#y'=69x^2(3x^5-4x^3+2)^22(5x^2-4)#

According to the chain rule,

#d/dx[u^23]=23u^22*(du)/dx#

Thus,

#y'=23(3x^5-4x^3+2)^22*d/dx[3x^5-4x^3+2]#

#=>23(3x^5-4x^3+2)^22(15x^4-12x^2)#

Factor out a #3x^2# from the last term.

#=>69x^2(3x^5-4x^3+2)^22(5x^2-4)#