query: $\frac{d^n}{dx^n}x^x=$?
positive_passages.docid: 22313
positive_passages.text: How should I calculate the $n$th derivative of $f(x)=x^x$?
negative_passages.docid: 43430
negative_passages.text: What exactly does $\frac{dx}{dy}$ mean?
negative_passages.docid: 113334
negative_passages.text: If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}= $?
negative_passages.docid: 128764
negative_passages.text: How does $y[x] = a x^r$ when $y'[x] = \frac{(r y[x])}{x}$ and $y[1] = a$
negative_passages.docid: 135731
negative_passages.text: Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
negative_passages.docid: 133614
negative_passages.text: Why is $x^{\log_x n}=n$?
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 152895
negative_passages.text: What is wrong with this derivation of $\frac{d}{dx}x^2$?
negative_passages.docid: 91059
negative_passages.text: Why is $\frac{d^n}{dx^n}(y(x))$ the notation for the $n$th derivative of $y(x)$, instead of $\frac{d^n}{d^nx}(y(x))$?
negative_passages.docid: 150642
negative_passages.text: How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
negative_passages.docid: 28297
negative_passages.text: derivative of x^x^x... to infinity?
negative_passages.docid: 88782
negative_passages.text: Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
negative_passages.docid: 104602
negative_passages.text: asymptotic of $x^{x^x} = n$
negative_passages.docid: 96875
negative_passages.text: Finding the value of $x^{x^2}+x^{x^6}$ given that $x^{x^4}=4$
negative_passages.docid: 128795
negative_passages.text: $n$th derivative of $e^x \sin x$
negative_passages.docid: 47026
negative_passages.text: if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$