# How do you differentiate #g(x)=(1+4x)^5(3+x-x^2)^8#?

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To differentiate the function ( g(x) = (1 + 4x)^5(3 + x - x^2)^8 ), you can use the product rule. First, differentiate each term of the product separately using the power rule and the chain rule, then multiply the results accordingly.

( g'(x) = 5(1 + 4x)^4 \cdot 4(3 + x - x^2)^8 + 8(1 + 4x)^5 \cdot (3 + x - x^2)^7(1 - 2x) )

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