1st derivative with ln function and fraction

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GregB

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Please help!! I am trying to figure out the first derivative of the following equation

v=((ln(S/62))/-0.015)*S

To solve S for the first derivative of the curve when v = 0

I know the approximate answer from plotting the curve of the equation, but the ln fraction is throwing me off - I believe the 1st derivative of ln(S/62) should be 1/(S/62), but then what do I do with this, and what happens to the -0.015? I believe the derivative of the lone S = 1. I could of course be wrong on all fronts.

I just seem to be going in circles and getting totally stuck! would appreciate some help, are my assumptions even correct?

TIA
 
Last edited:
GregB said:
...the first derivative of the following equation

v=((ln(S/62))/-0.015)*S

To solve S for the first derivative of the curve when v = 0
Click to expand...
What is meant by "solving S"? Are you maybe supposed to find the derivative of v "with respect to S"?

When you reply, please show your work so far. Thank you! ;)
 
stapel said:
What is meant by "solving S"? Are you maybe supposed to find the derivative of v "with respect to S"?

When you reply, please show your work so far. Thank you! ;)
Click to expand...

Hi Stapel, I’m by no means a mathematician so will try to explain as best I can. The relationship between v and S forms a bell-shaped curve. I need to fine the value of S where the slope = 0 and believe this is where the first derivative of the curve = 0. Let’s set S to be x if you like.
I.e. dv/dx = 0

I have broken it down as follows: letting 1/-0.015 be -0.015-1 then I have:
(ln(x/62)*-0.015-1)*x
I know the derivative of x is 1, but I’m having trouble applying the rules to this equation – is this the right approach to take? The two products are just confusing me.
 
GregB said:
I’m by no means a mathematician so will try to explain as best I can.
Click to expand...
It's not a matter of being a mathematician; using standard terminology is sufficient. For a start, is v a function of S, is S a function of v, or are they both a function of something else? With respect to which variable are you taking the derivative? Where did the "x" come from?

It may help to provide the full and exact text of the exercise, and the complete instructions. Thank you! ;)
 
stapel said:
It's not a matter of being a mathematician; using standard terminology is sufficient. For a start, is v a function of S, is S a function of v, or are they both a function of something else? With respect to which variable are you taking the derivative? Where did the "x" come from?

It may help to provide the full and exact text of the exercise, and the complete instructions. Thank you! ;)
Click to expand...

OK this is the best description I can give… v is a function of S and D whereby v=S*D. I have an equation for the relationship between v and D, and an equation for the relationship between v and S.

The v to D relationship is v=D*62e^(-0.015D), the derivative of which I have solved for a slope of 0.

The v to S relationship is v=ln(S/62)/(-0.015)*S which I need to solve for dv/dS=0, but this is where I am stuck.

I need these values as I need to calculate the value of c, which is S*D where the slope of each graph (equation) is zero.

I appreciate that this may not be a great explanation but it’s the best I have. I appreciate your help.
 
GregB said:
Please help!! I am trying to figure out the first derivative of the following equation

v=((ln(S/62))/-0.015)*S

To solve S for the first derivative of the curve when v = 0

I know the approximate answer from plotting the curve of the equation, but the ln fraction is throwing me off - I believe the 1st derivative of ln(S/62) should be 1/(S/62), but then what do I do with this, and what happens to the -0.015? I believe the derivative of the lone S = 1. I could of course be wrong on all fronts.

I just seem to be going in circles and getting totally stuck! would appreciate some help, are my assumptions even correct?

TIA
Click to expand...

Can you derive the expression of first derivative of the following function:

y = C * x * ln(x) ......[C is a constant]

dy/dx = ?
 
Subhotosh Khan said:
Can you derive the expression of first derivative of the following function:

y = C * x * ln(x) ......[C is a constant]

dy/dx = ?
Click to expand...

like this???:
a716467d8f6037aa21e89d0d45b9295b.png
.
 
Right - so you have:

v=((ln(S/62))/-0.015)*S

v= - (ln(S/62) * S * 1/0.015

v= - 1/0.015 * S * ln(S) + ln(62)/0.015 * S

Now differentiate.... term by term
 
So I get:
-1/0.015*lnS+ln62/0.015 which makes S=62, but I know from the graph this is incorrect
 
Subhotosh Khan said:
Right - so you have:

v=((ln(S/62))/-0.015)*S

v= - (ln(S/62) * S * 1/0.015

v= - 1/0.015 * S * ln(S) + ln(62)/0.015 * S

Now differentiate.... term by term
Click to expand...

dv/ds = 1/0.015*[ln(62) -ln(S)-1] = 0

ln(S) = ln[62/e] → S = ???
 
GregB said:
22.8. There's no way I would have figured this out, I need to go back and look at what you havedone. Thanks!
Click to expand...

Yes, there is a way. The last few steps are simply algebra - you have done those in high school.
 
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