# Differentiating natural logs and exponential functions?

1. Apr 13, 2009

### Mirth

Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate:

1: $$\frac{e^3^x}{\ln x}$$

I just don't know how to put it together... I know that $$e^3^x$$ is $$3e^3^x$$, and I know that you can't different $$\ln x$$, so I dunno what to do from there...

And:

2: $$\ln(e^-^2^x + e^-^x)$$

Totally not sure what to do there... Any help would be appreciated, I've looked online for similar examples and couldn't really find anything relevant to help me. Thanks!

2. Apr 13, 2009

### Hootenanny

Staff Emeritus
Let's take the first question first,
Correct.
Erm... yes you can!

HINT: Let y = lnx, then x = ey. Now differentiate x = ey with respect to x.

3. Apr 13, 2009

### Mirth

Hrm, I'm feeling a bit retarded so bear with me, hehe. So, $$\frac {1}{x}$$?

4. Apr 13, 2009

### Hootenanny

Staff Emeritus
Correct

So as far as putting it all together, can you suggest anything? Perhaps some sort of rule...?

5. Apr 13, 2009

### Mirth

I'm really retarded at math, ugh... Hehe. So I have $$\frac {3e^3^x}{1/x}$$ ... Pretty sure I'm lost on what to do from there. :(

6. Apr 13, 2009

### Hootenanny

Staff Emeritus
No that is not correct.

$$\frac{d}{dx} \frac{f\left(x\right)}{g\left(x\right)} \neq \frac{f^\prime\left(x\right)}{g^\prime\left(x\right)}$$

What 'rules' of differentiation do you know?

7. Apr 13, 2009

### Mirth

Not sure of any rules by name... I'm going to have to research more examples, I'm so rusty in math that I am unsure...

8. Apr 14, 2009

### Hootenanny

Staff Emeritus
Try searching for the quotient rule, or the product rule and chain rule.

9. Apr 14, 2009

### Mirth

I kinda give up on the first one, heh... Can someone tell me if I have #2 right?:

Answer: $$\frac {1 - e^-^2^x}{e^-^x + e^-^2^x}$$

10. Apr 14, 2009

### Pengwuino

The quotient rule and product rule explains how to differentiate two functions that divide are divided by or multiplied by eachother. Just look that up and identify f(x) and g(x) (that is the standard notation at least).

For #2, it isn't correct. What did you do to come up with that answer?

11. Apr 14, 2009

### slider142

Mirth, can you show us step by step how you differentiated that expression?

12. Apr 15, 2009

### tiny-tim

Hi Mirth!
ok, do you recognise this one by face

(fg)' = … ?