Differentiating

[seanac]

I have to differentiate the following with respect to x

 e^(4x) - e^(-5x)
-----------------
      e^(2x)

I really don't even know where to start with this.

In the given related example it has:

If y= e^(x) / (1 + x), find dy/dx

f = e^(x)         g= (1+x)
f'= e^(x)         g'= 1

(f/g)' = f'g - fg' / g^2
            
              e^(x) (1 + x) - e^(x) * 1
          =  ------------------------
                       (1 + x)^(2)

              e^(x) + x e ^(x) - e^(x)
          =  ------------------------
                      (1 + x)^(2)


               xe^(x)
          = -----------
             (1 + x)^(2)

    dy         xe^(x)
   ---   =   ---------
    dx       (1 + x)^(2)

But I am not sure how to use this formula for what I am doing. Do I split the

e^(4x) - e^(5x)
------------------ 
      e^(2x)

 into  

e^(4x)             e^(5x)
--------     and  --------
e^(2x)              e^(2x)

 

[mmm4444bot]

Can you please edit your post to put grouping symbols around all of the exponents ? Otherwise, I cannot know for sure what the exponents are without having to decipher the posted notation.

Cheers ~ Mark

 

[seanac]

Have I done what you wanted or is there other symbols you wanted me to use? Sorry if I have't followed what you said - I'm not used to writing out this kinda stuff on to a computer.

 

[mmm4444bot]

Have I done what you wanted Yes. Thank you for that.

or is there other symbols you wanted me to use? No. Parentheses are fine, thank you.

Sorry There is nothing in this thread for which you need to apologize.

Your idea to decompose the given ratio into a difference of two ratios is excellent because that simplifies to:

e^(2x) - e^(-7x)

How long has it been since you took algebra and precalculous ?

 

[seanac]

I'm from New Zealand, we follow an NCEA system where you do Level 1, Level 2 and Level 3. I am doing Level 3 Calculus but I haven't done math since Level 2 which I did in 2008. Because of personal reasons I was unable to attend school during 2009. Due to the large gap between Level 2 and Level 3 I am struggling to remember a lot of the work. Suffice it to say I am finding Level 3 challenging, I really don't have a mind for math at the best of times and find many concepts hard to follow/remember.

 

[mmm4444bot]

Okay, it sounds to me like New Zealand schools are as bad as United States schools in letting students enroll into courses for which they are not prepared. (If you were my student, I would advise you to start over at Level I or test into Level 2.)

When we have a ratio of exponential expressions, where the bases are identical, there is a property for that.

x^n/x^m = x^(n - m)

e^(4x)/e^(2x) = e^(4x - 2x)

Good to go?