Natural Log Differentiation

**CrEpE** · April 6th 2010, 08:05 PM

I have a problem here that I am not sure is correct.

We have been asked to find the derivative of the following funciton:

ln{(x(x^2+5))/sqrt(x^3-5)}
I realize this looks really sloppy.

The answer that I have arrived at is

{((2x^2 + 5) - sqrt(3x^2))/2}

Any help would be greatly appreciated

**Anonymous1** · April 6th 2010, 08:07 PM

Originally Posted by CrEpE

I have a problem here that I am not sure is correct.

We have been asked to find the derivative of the following funciton:

ln{(x(x^2+5))/sqrt(x^3-5)}
I realize this looks really sloppy.

The answer that I have arrived at is

{((2x^2 + 5) - sqrt(3x^2))/2}

Any help would be greatly appreciated

$\frac{d}{dx}ln({\frac{x(x^2+5)}{\sqrt{x^3-5}}}) = \frac{\sqrt{x^3-5}}{x(x^2+5)}\times \frac{d}{dx}[\frac{x(x^2+5)}{\sqrt{x^3-5}}]$ $= \frac{\sqrt{x^3-5}}{x(x^2+5)}\times \frac{\sqrt{x^3-5}\frac{d}{dx}[x(x^2+5)] - x(x^2+5)\frac{d}{dx}[\sqrt{x^3-5}]}{(\sqrt{x^3-5})^2}$

Can you take it from here?

**CrEpE** · April 6th 2010, 08:17 PM

Yes I believe so. Maybe I just oversimplified it

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