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

Answer 1

William Abdalla

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

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

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

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

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Answer 2

Paisley Johnson

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.