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How do you find the derivative of #(1+4x)^5(3+x-x^2)^8# using the chain rule?

1 Answer

Nov 1, 2016

#y'=8(1-2x)(1+4x)^5(3+x-x^2)^7 +20(1+4x)^4(3+x-x^2)^8#

Explanation:

#y=(1+4x)^5 (3+x-x^2)^8#

Use product rule #(fg)'=fg'+gf'# and chain rule #(f(g(x))'=f'(g(x))*g'(x)#

#f=(1+4x)^5,# #g=(3+x-x^2)^8#

#f'=5(1+4x)^4 * 4,# #g'=8(3+x-x^2)^7 * (1-2x)#

#y'=fg'+gf'#

#y'=8(1-2x)(1+4x)^5(3+x-x^2)^7 +20(1+4x)^4(3+x-x^2)^8#

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