Logarithmic functions help.

• March 17th 2008, 02:27 PM
RedBarron
Logarithmic functions help.
Im taking Business calc so it's not nearly as hard as normal calc, and I have a few questions on a take home quiz I have. If any one could help me it would be greatly appreciated.

Find the derivative, do not need to simplify

g(x)=ln(2x-3/x^2-4)

and f(x)=(ln(12x^2+5))^25

lastly y=e^x ln(5x)

Thanks a lot, im pretty much done with the quiz im just not sure on these 3 probs (Headbang)
• March 17th 2008, 03:55 PM
o_O
Some of the questions are a bit ambiguous but seems like they involve the application of the chain rule which says:
$\left[f(g(x))\right]' = f'\left(g(x)\right) \cdot g'(x)$

For: $y = ln\left(\frac{2x-3}{x^{2}-4}\right)$
Let: $f(x) = ln(x) \quad \quad g(x) = \frac{2x - 3}{x^{2}-4}$

Applying the formula:
$\left[ ln\left(\frac{2x-3}{x^{2}-4}\right) \right]' = \underbrace{\frac{1}{g(x)}}_{(\ln x)' = \frac{1}{x}} \cdot \: \:g'(x)$
$= \frac{1}{\frac{2x - 3}{x^{2}-4}} \cdot \left(\frac{2x-3}{x^{2}-4}\right)'$
$= \frac{x^{2} - 4}{2x - 3} \cdot \underbrace{\left(\frac{2x-3}{x^{2}-4}\right)'}_{\mbox{Quotient Rule}}$

See if you can apply the chain rule to the other questions.