What is the derivative of $f(x)=ln[x^9(x+3)^6 (x^2+7)^5]$ ?

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Answer 1 · 2015-10-18T05:01:25

Use the properties of logarithms to rewrite:

$f(x)=ln[x^9(x+3)^6 (x^2+7)^5]$

$= ln(x^9)+ln(x+3)^6+ln(x^2+7)^5$

$= 9ln(x)+6ln(x+3)+5ln(x^2+7)$

So,

$f'(x) = 9/x+6/(x+3)+5/(x^2+7) 2x$

Simplify algebraically as desired.

What is the derivative of f(x)=ln[x^9(x+3)^6 (x^2+7)^5]f(x)=ln[x^9(x+3)^6 (x^2+7)^5]?