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To gain full voting privileges, It is nice to use the definitions According to symbolic matlab and wolframalpha, $\\frac{\\partial x(t)}{\\partial x} = 0, \\frac{\\partial x}{\\partial x} = 1$ i came across this while trying to.

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Okay this may sound stupid but i need a little help.what do $\\large \\frac{d}{dx}$ and $\\large \\frac{dy}{dx}$ mean All other answers are very good, but here is just another way to see it that can be very useful I need a thorough explanation

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Rankeya has given a valid answer to the written question, but i realize now i was too vague

Secondly, i looked up the correct exercise in jacobson and found that the following exercise is precisely to show that it does hold for all division rings Stupid gut feelings.i'm accepting this answer and reposting the correct question. I understand the meaning of $\frac {dy} {dx}$ and $\int f (x)dx$, but outside of that what do $dy, du, dx$ etc. When i took calc i, derivatives and integrals.

As noted in the comments, your derivation contains a mistake To answer the question, this function can not be integrated in terms of elementary functions So there is no simple answer to your question, unless you are willing to consider a series approximation, obtained by expanding the exponential as a series $$\int {x^xdx} = \int {e^ {\ln x^x}dx} = \int {\sum_ {k=0}^ {\infty}\frac {x^k\ln.

Observe that for a continuous random variable, (well absolutely continuous to be rigorous)

$$\mathsf p (x> x) = \int_x^\infty f_x (y)\operatorname d y$$ then taking the definite integral (if we can) $$\int_0^\infty \mathsf p (x> x)\operatorname d x = \int_0^\infty \int_x^\infty f_x (y)\operatorname d y\operatorname d x$$ to swap the order of integration we use tonelli's theorem, since a.