# Differentiating natural logs and exponential functions?

• Mirth
In summary, Mirth said that she was having a hard time figuring out a problem in which she had to differentiate, and she listed incorrect rules of differentiation that she recognized.

#### 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 don't know 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!

Let's take the first question first,
Mirth said:
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 $$3e^3^x$$
Correct.
Mirth said:
and I know that you can't different $$\ln x$$, so I don't know what to do from there...
Erm... yes you can!

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

Hootenanny said:
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.

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

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

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

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. :(

Mirth said:
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. :(
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?

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...

Mirth said:
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...
Try searching for the quotient rule, or the product rule and chain rule.

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

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

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

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

The quotient rule and product rule explains how to differentiate two functions that divide are divided by or multiplied by each other. 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?

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

Hi Mirth!
Mirth said:
Not sure of any rules by name...

ok, do you recognise this one by face

(fg)' = … ?