Normally I would know how to get a simple log derivative, but this problem is much more difficult. $\displaystyle ln \frac{x^2\sqrt{4x+1}}{(x^3+5)^3}$
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Originally Posted by radioheadfan Normally I would know how to get a simple log derivative, but this problem is much more difficult. $\displaystyle ln \frac{x^2\sqrt{4x+1}}{(x^3+5)^3}$ Let $\displaystyle g(x)= \ln f(x)$ represent the given fuction. The derivitive is then $\displaystyle [1/f(x)]\cdot f^\prime (x).$ Use the Quotient Rule or Product Rule for the last bit.
Originally Posted by radioheadfan Normally I would know how to get a simple log derivative, but this problem is much more difficult. $\displaystyle ln \frac{x^2\sqrt{4x+1}}{(x^3+5)^3}$ Use the usual log rules to get an expression that is simpler to differentiate. Edit: By the way, you better note that $\displaystyle \ln x^2 = 2 \ln |x|$.
Originally Posted by mr fantastic Use the usual log rules to get an expression that is simpler to differentiate. Or that...
I used the log rules and got 2/3
Originally Posted by radioheadfan I used the log rules and got 2/3 What happened to all the x's?
Originally Posted by radioheadfan I used the log rules and got 2/3 Don't think that's right... Using the log rules, we get $\displaystyle \ln x^2 + \ln\sqrt{4x+1} - \ln[(x^3+5)^3]$ $\displaystyle =2\ln|x| +\frac{1}{2}\ln(4x+1) -3\ln(x^3+5).$ Now differentiate...
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