Question #915d1

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Answer 1 · 2017-02-06T13:17:54

For #f(x) = uv#, the product rule says #f'(x) = u'v+uv'#

Also, the chain rule tells us that #d/dx(u^n) = n u^(n-1) (du)/dx#.

Putting these together, we get

#f'(x) = 3(x+2)^2 (1) x^2 + (x+2)^3 2x#

We can clean this up a bit.

#f'(x) = 3x^2(x+2)^2 +2x(x+2)^3#.

We can make it nicer by removing the common factors from the two terms and simplifying what's left.

#f'(x) = [3x^2(x+2)^2 +2x(x+2)^3]#

# = x(x+2)^2[3x + 2(x+2)]#

# = x(x+2)^2 [5x+4]#

# = x(x+2)^2 (5x+4)#