Taking derivative of a function times a log

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• March 13th 2010, 03:25 PM
ajcadoo
Taking derivative of a function times a log
y=2xlog base 10(rootx)
What are the proper steps for solving this?
• March 13th 2010, 03:43 PM
skeeter
Quote:

Originally Posted by ajcadoo
y=2xlog base 10(rootx)
What are the proper steps for solving this?

$y = 2x \log_{10}{\sqrt{x}}$

$y = x \log_{10}{x}$

$y = x \cdot \frac{\ln{x}}{\ln{10}}$

$y = \frac{1}{\ln{10}}\left(x \ln{x}\right)$

$y' = \frac{1}{\ln{10}}\left(x \cdot \frac{1}{x} + \ln{x}\right)$

$y' = \frac{1}{\ln{10}}\left(1 + \ln{x}\right) = \frac{1+\ln{x}}{\ln{10}}$