Do you remember ODE-
Ordinary Differentiate Equation?
Do you like to be reminded of
How much a fine mathematician
love to work on math as if one is a magician?
Let me teach you
about how to differentiate a polynomial
By the power rule.
The rate of change in distances at certain time period is called speed,
The rate of change in the increase of population is called average growth,
How about the rate of change in each second?
The way to calculate the instant rate of change
Is to differentiate…
For a polynomial,
The derivatives to any fixed number or constant
Is zero,
The derivative to 1 is zero,
The derivative to 2 is again zero,
The derivative to 200 is also zero..
What a hero.
The derivatives to any power of x
Is to bring down the power as a coefficient,
Reduce the power to x by one.
For example,
The derivative of x to the power 5
Is 5 times x to the power 4…
Do you get it?
Did you picture it?
The derivative of x to the power 2
Is 2 times x to the power 1,
Which is the same as 2 times x or 2x,
How divine!
If you stick to the rule,
You can do it correct and feel cool.
Keep working on it,
Keep thinking of it,
You will make it,
…
Thanks to Trisha, Fiveloaf, and Pravin who have nominated Jingle for The PERFECT Poet Award , which Jingle feels very honored and accepts here, Please visit them to read their OUTSTANDING work in poetry today…
For Week 27 The Perfect Poet Award, Jingle wishes to nominate (she is nominated by 3 poets, thus decides to nominate three poets here.)
Congratulations! Tracy, Leonnyes, and JP, I enjoy your talent in writing or poetry and feel very blessed to have you join Poets Rally Week 26…
*****
I wold like to make an announcement about Pravin Nair whose poetry has been published as a book!
The link to Pravin Nair’s book publishing announcement:
http://www.versepoems.com/2010/08/and-my-book-is-born.html
Let’s Celebrate by visiting her and give her the greetings and love she deserves! cheers!
*****
d dx |
x^{n} = nx^{n−1} |
“The derivative of a power of x
x with the exponent reduced by 1.”
That is called the power rule. For example,
d dx |
x^{5} | = 5x^{4} |
However, we know that the power rule is true when n = 1:
d dx |
x^{1} | = 1· x^{0} = 1; | ||
that it is true when n = 2: | ||||
d dx |
x^{2} | = 2x; | ||
and that it is true when n = 3 : | ||||
d dx |
x^{3} | = 3x². |
It seems natural, then, to give a proof by induction; The induction hypothesis will be that the power rule is true for n = k:
d dx |
x^{k} | = k x^{k−1}, |
and we must show that it is true for n = k + 1; i.e. that
d dx |
x^{k+1} | = (k + 1) x^{k}. |
Now,
d dx |
x^{k+1} | = | d dx |
x· x^{k} |
d dx |
x^{k+1} | = | x· k x^{k−1} + x^{k}· 1, | |
d dx |
x^{k+1} | = | k x^{k} + x^{k} | |
d dx |
x^{k+1} | = | (k + 1)x^{k}. |
Therefore, if the power rule is true for n = k, then it is also true for its succesor, k + 1. And since the rule is true for n = 1, it is therefore true for every natural number.
Problem. Calculate the derivative of x^{6} − 3x^{4} + 5x^{3} − x + 4.
Whooohooo….congrats to all the nominees and thanks for this beautiful post Ji. Love to all xx
I appreciate your encouragement, Amanda!
Thank you, Jingle, for the nomination…I’m very touched that you chose to nominate ME out of all the poets that you are involved with through your wonderful community…Thank You! 🙂 You know…… YOU ROCK 🙂
Sincerely,
Tracy H
U r welcome,
u deserve it,
🙂
What a post!!! I am downloading it (with your permission ofcourse)… I can use it to teach my hubby some decent Math .. heheheh
So cutely you’ve put it, Ji!! You are the coolest! 🙂
Thank you for the lovely awards… I am in the process of putting them up!!! Yaaayyyy
feel free to download anything here…
🙂
Congratulations all around … and Jingle thanks for the poem, the problem, and the heads up on Pravin’s book. Hooray … all good stuff! 🙂
Thanks, Jamie!
😉
Hi, Ji! I think you want my nomination for next Rally’s Perfect Poet. (Referring to the message on my blog ths a.m.) That would be frayededges.
fell off seating
fellow see things
feel of sea thing
bellow seething
below seating
underneath the city
I would need a magician to do that math.
I wonder if the Universe would put one in my path?
I can easily Differentiate
because it takes a good teacher
to give everyone the same concept on a unique plate
wow,
nice to see you.
😉
congratulation for the nomination and good work with mathematics poem… I never looked at maths that way…
cheers!!!
I appreciate your kind words.
😉
you so very much deserve the award! you are the first nominee- for all the weeks.
loved the mathemagic post. 🙂
too hard to digest for many,
I was kind of crazy…
🙂
brilliant, u deserve all these awards, im chuffed for you.xxx
William,
thanks a lot!
😉
Hi jingle..thts a real cool poem…Always had this fear of amthematics.. now will see it in a new light 🙂
And I must must thank you for mentioning about my book..Im honoured, flattered and humbled..thnk you so much !
Ive nt been so regular on my blog or on ur wonderful forum these days due to professional, personal reasons….But believe me, I am trying my best!
thnks once again Jingle for the best wishes!
I truly am grateful what you’re doing here!