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Hi;
Differentiate y=a^x by using ln and e???
Malik
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hi,
If you take logs of both sides (base e) then
Differentiate with respect to x:
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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logs of both sides (base e) why you don't wright lne???
Malik
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are different ways of writing the same thing. ln was the quickest for me. (But not as it turned out, as I've had to add this post )
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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Is it possible y=e^(alnx)???
Malik
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Is it possible y=e^(alnx)???
You can differentiate this:
Replacing the first part by y brings you back to my earlier answer.
My version is the one that you will find in lists of standard differentials such as:
http://www.math.wustl.edu/~freiwald/131 … etable.pdf
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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I know these all formulas!!!
Malik
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I also know the simple method u do on top but confused in notes about y=e^(alnx)???
Malik
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Your 2nd step of implies that confusing me !!!
Because we must balance eq when we add any value we also subtract so ???
Malik
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Why e^(lny)=y
Malik
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We have met this before. ln and e^ are inverse functions.
If y = e^x then x = ln(y)
So if you raise ln(something) to the power of e, the ln and e cancel out, and you're left with the 'something' ... in this case just y
It's like doubling one half of something. Doubling 'undoes' the effect of halving so you get back to where you started.
One way to define a log is to say it has this property.
eg If y = a^x then we define the log of y (in base a) to be x.
Or you can say, if I have a number y, what power of 'a' will give me y. This power of 'a 'is called the log of y.
eg. What power of 10 will give me 1000 ? Answer 3. So we say 3 = log(1000) in base 10.
So you can always re-write a power expression as a log expression or the other way round.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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ln and e^ are inverse functions
E hat??
Malik
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to the power of e some say exp
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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Exponent? ?
Malik
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Not exactly. Microsoft Excel uses it to mean:
You will find a lot of helpful maths on this site:
http://www.mathsisfun.com/algebra/expon … ithms.html
When you want a new topic, use the search engine at the top of every page, or the cross-links between pages.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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Microsoft exel?? How come there
Last edited by Zeeshan 01 (2017-04-29 04:05:06)
Malik
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Well it is. I don't know why you're surprised. Am I missing something? If you have that software then give it a try. If you don't then stop worrying.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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I used this software when I am 6 days old !!! HEHEHE MICROSOFT all applications
Malik
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Useful tool
Malik
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