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How do you differentiate #f(x) = ln [ x^{2}(x + 3)^{8}(x^2 + 4)^{3} ]#?

1 Answer

Apr 29, 2015

I'll leave it to someone else to use #d/dx(lnu) = 1/u (du)/dx# and the three factor product rule. I'll do it the easy way:

#f(x) = ln [ x^{2}(x + 3)^{8}(x^2 + 4)^{3} ]#

#f(x) = ln x^2+ln(x + 3)^8 + ln(x^2 + 4)^3#

#f(x) =2 ln x + 8 ln(x + 3) +3 ln(x^2 + 4)#

So
#f'(x) = 2/x + 8/(x+3) +3/(x^2+4) *(2x)#

#f'(x) = 2/x + 8/(x+3) +(6x)/(x^2+4)#.

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