# Derivative of e^5X - 3log(x)

1. Feb 20, 2006

### nofunatall

How do you find the derivative of the following?

e^5X - 3log(x)

2. Feb 20, 2006

### Zurtex

Do you know how to use the chan rule and what the derivative of a log is?

3. Feb 20, 2006

### nofunatall

Learned years ago. In other words. No.

4. Feb 20, 2006

### Zurtex

Well:

$$\frac{d}{dx} ( \log x ) = \frac{1}{x} \quad \text{for all} \, x > 0$$

The chain rule goes:

$$\frac{dg}{dx} = \frac{dg}{df} \frac{df}{dx}$$

Or using Newton notation, if there exists some y = g(f(x)) then y' = f'(x) g'(f(x))

5. Feb 20, 2006

### nofunatall

Got that part. That makes sense.

6. Feb 21, 2006

### bomba923

~No, that's not true;

$$\forall x > 0, \; \frac{d}{{dx}}\ln x = \frac{1}{x}$$

$$\forall x > 0, \; \frac{d}{{dx}}\log x = \frac{1}{{x\ln 10}}$$

The natural logarithm of $x$ is written as $\ln(x)$, not $\log(x)$.

log(x) is the base 10 logarithm,
$$\log x = \frac{{\ln x}}{{\ln 10}}$$

Last edited: Feb 21, 2006
7. Feb 21, 2006

### Moo Of Doom

Not in all cases. For example, it is usual in analysis to use just log to mean base e. Sadly, this does cause some confusion, so people really should write the base when there's no context.

8. Feb 21, 2006

### Zurtex

Hmm, I've not seen log mean log10 in a good year or so now, I'm so used to log meaning loge I just assumed this was the case. I still think it does, but only the original poster will be able to tell us.

9. Feb 21, 2006

### matt grime

log should always be taken to mean log base e unless in certain very strict cases none of which are applicable in anaysis. certainly very few people in mathematics would ever write ln for natural log unless close by they had a need to use logs in other bases (see below)

short of the occasional use in engineering/applied maths no one uses base 10, and in fact the most natural second choice after e ought to be base 2.

10. Feb 21, 2006

### 0rthodontist

My algorithms textbook uses three different kinds of logarithm, log, ln, and lg for base 2. I thought that was especially unusual because in algorithms it usually doesn't matter what base you're using.

Last edited: Feb 21, 2006
11. Feb 21, 2006

### arildno

How horrid, and utterly dumb.

I still remember how shocked I was in a class of fluid mechanics where my professor almost apologetically said that a particular formula used Briggsian logarithms rather than the natural one.
(It was a typical "engineer" formula).