# Derivative of log

• April 9th 2012, 01:49 PM
loghater
Derivative of log
Find where y'=0 given that y=10^xlogx-10x
• April 9th 2012, 02:12 PM
Plato
Re: Derivative of log
Quote:

Originally Posted by loghater
Find where y'=0 given that y=10^xlogx-10x

The derivative is $y'=10^x\log(10)\log(x)+\frac{10^x}{x}-10$.
The solution by inspection is clear.
• April 9th 2012, 02:22 PM
loghater
Re: Derivative of log
How do you get x? I got to the point where (10^xlogx-10x)/logxln10x=0
• April 9th 2012, 02:31 PM
Plato
Re: Derivative of log
Quote:

Originally Posted by loghater
How do you get x? I got to the point where (10^xlogx-10x)/logxln10x=0

That derivative is not correct.
• April 10th 2012, 06:51 AM
HallsofIvy
Re: Derivative of log
Quote:

Originally Posted by loghater
Find where y'=0 given that y=10^xlogx-10x

Important question- is "log x" the common logarithm (base 10) or the natural logarithm (base e)? Normally, for a calculus problem I would assume natural logarithm, but the presence of "10^x" makes me ask.

I presume you know that the derivative of -10x is -10.

10^x log x is a product so use the product rule: (10^x log x)'= (10^x)' log x+ 10^x (log x)'.

The derivative of 10^x is (10^x)'= (10^x) ln x and the derivative of log x is
1) 1/(x ln(10)) if it is common logarithm.
2) 1/x, if it is natural logarithm.
• April 10th 2012, 07:40 AM
Prove It
Re: Derivative of log
Quote:

Originally Posted by loghater
Find where y'=0 given that y=10^xlogx-10x

As it is written, there is no way to tell whether the original function is \displaystyle \begin{align*} y = 10^x\log{x} - 10x \end{align*} or \displaystyle \begin{align*} y = 10^{x\log{x}} - 10x\end{align*} or even something else. The OP needs to clarify, and in future, needs to use brackets or at the very least, some space, where they are needed, or even better, to learn some basic LaTeX.