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2h
revised Differentiate the Function: $f(x)=\ln (\sin^2x)$
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2h
comment Differentiate the Function: $f(x)=\ln (\sin^2x)$
Now you've cancelled wrong at the last step.
3h
comment Differentiate the Function: $f(x)=\ln (\sin^2x)$
That explains the $\sin^2 x$ in the denominator, not the second $\sin^2 x$ in the first line of the computation of $f'(x)$. As for the downvote, it is possible the person doesn't like the formatting that I did (or didn't like the format before.)
3h
comment Differentiate the Function: $f(x)=\ln (\sin^2x)$
Not clear where you get the $\sin^2 x$ in the numerator.
3h
revised Differentiate the Function: $f(x)=\ln (\sin^2x)$
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15h
revised What's book that I should read?
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1d
revised Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
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1d
revised Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
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1d
awarded  Nice Answer
1d
comment Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
Better to just keep fractions - decimal notation often gives the impression of being approximations.
1d
revised Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
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1d
revised Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
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1d
comment Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
Isn't it easier to just show that if $p,q$ relatively prime, then $p^2$ and $q^2$ are relatively prime. And $2n+1$ and $n$ are relatively prime, so $p^2=2n+1$ and $q^2=n$. You just need to know that every rational number has a unique representation as a quotient of relatively prime numbers.
1d
answered Prove or disprove that $\sqrt{2+\frac{1}{n}}$ is irrational for $n \in \mathbb{Z}^+$
1d
comment A few questions on the later chapters in Principles of Mathematical Analysis by Walter Rudin (3rd Edition)
It would help to remind us what those chapters cover. I remember personally disliking his coverage of differential forms and Stokes. I hadn't taken any several variables classes, so I had no idea what was going on other than pure abstract nonsense.
1d
revised When solving trigonometric irrational equations does the condition of existence of the radicand under an even root matter?
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1d
answered When solving trigonometric irrational equations does the condition of existence of the radicand under an even root matter?
1d
revised When solving trigonometric irrational equations does the condition of existence of the radicand under an even root matter?
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2d
revised what is the definition of numbers?
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2d
comment what is the definition of numbers?
In general, the term "number" is used fairly loosely in mathematics, unfortunately, so there isn't a general rule.