- #1
ttpp1124
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- Homework Statement
- can someone check to see if my work is correct?
- Relevant Equations
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Differentiate, but do not simplify: ##y=3ln(4-x+5x^2)##
- Thread starter ttpp1124
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- Differentiate Simplify
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The discussion centers on differentiating the function y=3ln(4-x+5x^2). Participants express confusion over the presence of a "u" term in the differentiation process, questioning whether it was a typo. There is also a debate about the necessity of simplifying the expression, with some asserting it appears simple enough already. The conversation encourages the use of LaTeX for clarity in mathematical expressions and offers support for those struggling with the notation. Overall, the thread emphasizes the importance of accurate differentiation while maintaining the original complexity of the expression.
- #2
DaveE
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It looks like there's a "u" term in your answer but none in the original problem. A typo?
- #3
ttpp1124
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please excuse me horrible writing, it's supposed to be a 4DaveE said:
- #4
DaveE
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OK, then I'm happy. I'm not sure about the do not simplify part, it looks pretty simple already!
- #5
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ttpp1124 said:
A solution to this problem is by using Latex. It is really not that hard: write what you would expect and put it between double hashtags:
I promise we will be there to help you learn it if you struggle!
- #6
DaveE
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What part of this calculation were you not confident about? Why do you ask, instead of knowing you are correct?
First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...
It's easy to see that any polynomial is function of that class. Also it seems that composition of exponent and polynomial is good as well. G_f(a, b) should be equal G_f(b, a) as the f(a+b) is symmetrical.
Does anyone have information about this or at least related to it?