Differentiating natural logs and exponential functions?by Mirth Tags: differentiating, exponential, functions, logs, natural 

#1
Apr1309, 03:12 PM

P: 23

Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate:
1: [tex] \frac{e^3^x}{\ln x} [/tex] I just don't know how to put it together... I know that [tex]e^3^x[/tex] is [tex]3e^3^x[/tex], and I know that you can't different [tex]\ln x[/tex], so I dunno what to do from there... And: 2: [tex] \ln(e^^2^x + e^^x)[/tex] 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
Apr1309, 03:43 PM

Emeritus
Sci Advisor
PF Gold
P: 9,789

Let's take the first question first,
HINT: Let y = lnx, then x = e^{y}. Now differentiate x = e^{y} with respect to x. 



#3
Apr1309, 04:18 PM

P: 23





#4
Apr1309, 04:20 PM

Emeritus
Sci Advisor
PF Gold
P: 9,789

Differentiating natural logs and exponential functions?So as far as putting it all together, can you suggest anything? Perhaps some sort of rule...? 



#5
Apr1309, 04:50 PM

P: 23

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




#6
Apr1309, 04:57 PM

Emeritus
Sci Advisor
PF Gold
P: 9,789

[tex]\frac{d}{dx} \frac{f\left(x\right)}{g\left(x\right)} \neq \frac{f^\prime\left(x\right)}{g^\prime\left(x\right)}[/tex] What 'rules' of differentiation do you know? 



#7
Apr1309, 06:43 PM

P: 23

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
Apr1409, 02:38 AM

Emeritus
Sci Advisor
PF Gold
P: 9,789





#9
Apr1409, 04:18 PM

P: 23

I kinda give up on the first one, heh... Can someone tell me if I have #2 right?:
Answer: [tex]\frac {1  e^^2^x}{e^^x + e^^2^x} [/tex] 



#10
Apr1409, 05:01 PM

PF Gold
P: 7,125

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



#11
Apr1409, 05:03 PM

P: 876

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



Register to reply 
Related Discussions  
Natural Logs and inverse functions  Calculus & Beyond Homework  2  
Functions + Natural Logs  Precalculus Mathematics Homework  6  
Differentiating Logarithmic and Exponential Functions  Calculus & Beyond Homework  10  
differntiating natural logs of x and y functions  Precalculus Mathematics Homework  6  
differentiating natural logs  Precalculus Mathematics Homework  5 