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Apost8

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I have a tricky derivative HW problem I'm working and am hoping someone might tell me if I'm doing this correctly or not. Thanks in advance!

Find g'(x) where g(x) = [(1+4x)^5] X [(-x^2+x+3)^8)]

By the product rule, I get:

g'x = [(d/dx((1+4x)^5)) X (-x^2+x+3)^8] + [(d/dx(-x^2+x+3)^8) X (1+4x)^5)]

Then, using the chain rule I get:

g'(x) = [((d/dx((1+4x)^5))(d/dx(1+4x))) X (-x^2+x+3)^8] + [((d/dx((-x^2+x+3)^8))(d/dx(-x^2+x+3))) X ((1+4x)^5)]

Giving:

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

Then it should just be a matter of simplifying algebraically. Right?

Find g'(x) where g(x) = [(1+4x)^5] X [(-x^2+x+3)^8)]

By the product rule, I get:

g'x = [(d/dx((1+4x)^5)) X (-x^2+x+3)^8] + [(d/dx(-x^2+x+3)^8) X (1+4x)^5)]

Then, using the chain rule I get:

g'(x) = [((d/dx((1+4x)^5))(d/dx(1+4x))) X (-x^2+x+3)^8] + [((d/dx((-x^2+x+3)^8))(d/dx(-x^2+x+3))) X ((1+4x)^5)]

Giving:

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

Then it should just be a matter of simplifying algebraically. Right?

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