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2. What do the symbols d/dx and dy/dx mean?

   math.stackexchange.com/questions/340744

   The symbols d/dx and dy/dx represent derivatives in calculus, indicating rates of change with respect to a variable.

3. Rigorous proof that $dx dy=r\\ dr\\ d\\theta$

   math.stackexchange.com/questions/1636021

   Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

4. Derivative of sigmoid function $\\sigma (x) =...

   math.stackexchange.com/questions/78575

   In my AI textbook there is this paragraph, without any explanation. The sigmoid function is defined as follows $$\\sigma (x) = \\frac{1}{1+e^{-x}}.$$ This function is easy to differentiate

5. matrices - Differentiate $f(x)=x^TAx$ - Mathematics Stack...

   math.stackexchange.com/questions/312077

   Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

6. What does the dx mean in an integral? [duplicate]

   math.stackexchange.com/questions/1329131

   It's because an integral means you are summing over a lot of very thin rectangles under a curve. The height of the rectangle is f(x) and the width is called $\delta x$ (These two symbols should be read as a single symbol, it doesn't mean $\delta \times x$).

7. solving the integral of $e^ {x^2}$ - Mathematics Stack Exchange

   math.stackexchange.com/questions/1242056/solving-the-integral-of-ex2

   Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

8. How to change order of integration in a double integral?

   math.stackexchange.com/questions/467910

   How would you go about changing the order of integration in a function say ; $$\int_0^8\int_\sqrt[3]{y}^2 f(x,y)~dx~dy$$

9. Why is $dy dx = r dr d \\theta$ - Mathematics Stack Exchange

   math.stackexchange.com/questions/49927

   Possible Duplicate: Explain $\\iint \\mathrm dx\\mathrm dy = \\iint r \\mathrm d\\alpha\\mathrm dr$ I'm reading the proof of Gaussian integration. When we change to polar coordinates, why do we get an "

10. Limit of $\\frac{x^c-c^x}{x^x-c^c}$ as $x \\rightarrow c$

    math.stackexchange.com/questions/2689167/limit-of-fracxc-cxxx-cc-as-x-rightarrow-c

    My question is: Show that $\lim_{x \rightarrow c} \frac{x^c-c^x}{x^x-c^c}$ exists and find its value. Because the limit is 0/0 I've tried using L'Hopital's rule, but every time I differentiate it I

11. Integral: $\\int_{-\\infty}^{\\infty} x^2 e^{-x^2}\\mathrm dx$

    math.stackexchange.com/questions/66084

    I don't know how to evaluate it. I know there is one method using the gamma function. BUT I want to know the solution using a calculus method like polar coordinates. $$\\int_{-\\infty}^\\infty x^2 e^...