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!(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Chain/Product rule

**Physics Forums | Science Articles, Homework Help, Discussion**