12-12-2004, 03:03 PM | #1 (permalink) |
Psycho
Location: Dreams
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Quick Higher Derivative Problem
find y''' if y=(2x+3)^1/2 (or the square root of 2x+3)
the answer in the book is 3(2x+3)^-5/2 but I can't seem to arrive at this, my number where the first 3 is located is different. Calc midterm tomorrow (and then final tues.!) and I hate learning stuff like this all in one day
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I know not how I may seem to others, but to myself I am but a small child wandering upon the vast shores of knowledge, every now and then finding a small bright pebble to content myself with. [Plato] |
12-12-2004, 04:04 PM | #3 (permalink) |
Psycho
Location: Dreams
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can you explain a bit more?
if the derivative of x^n = nx^n-1 then wouldn't f'(x)=1/2(2x+3)^-1/2 ? I guess having the power outside the parenthesis is confusing me.
__________________
I know not how I may seem to others, but to myself I am but a small child wandering upon the vast shores of knowledge, every now and then finding a small bright pebble to content myself with. [Plato] |
12-12-2004, 05:15 PM | #5 (permalink) |
Psycho
Location: Dreams
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Ok I think I got this problem licked, thanks for the help and wish me luck tomorrow
__________________
I know not how I may seem to others, but to myself I am but a small child wandering upon the vast shores of knowledge, every now and then finding a small bright pebble to content myself with. [Plato] |
12-12-2004, 06:19 PM | #7 (permalink) | |
Psycho
Location: Atlanta, GA
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Quote:
f(x) = sin x f'(x) = cos x f''(x) = - sin x = - f(x) f'''(x) = - f'(x) = - cos x and so on... But for the most part I think you just have to do it the long way.
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"Great spirits have always encountered violent opposition from mediocre minds" -- Albert Einstein "A clear indication of women's superiority over man is their refusal to play air guitar." --Frank Zappa |
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12-12-2004, 07:06 PM | #8 (permalink) | |
Addict
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Quote:
D^n x^k = (k)_n x^{k-n}, where (k)_n is the falling factorial of k to n, namely, (k)_n = k (k-1) (k-2) ... (k-n+1) if n>0; (k)_0 = 1. Another useful formula is Leibniz' Rule, which is a generalization of the product rule, and looks like this: D^n (f(x)g(x)) = \sum_{i=0}^n \binom{n}{i} f^(i)(x) g^(n-i)(x), where \binom{n}{i} is the binomial coefficient, and f^(i) is the ith derivative of f. Note its relation to the binomial theorem, making it easy to remember. Graphically, There's also a generalization of the chain rule, but I can't remember it and it's sort of ugly anyway. Last edited by phukraut; 12-13-2004 at 12:26 AM.. |
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Tags |
derivative, higher, problem, quick |
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