# Tagged Questions

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### Explain this chain rule for differentiating $y=xe^{-kx}$

I am asked to differentiate $$y=xe^{-kx}$$ The answer I am given is $$e^{-kx}(-kx+1)$$ I understand that when e is differentiated, it remains the same. I also see the product rule, but I'm not sure ...
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### Is this Euler-Mascheroni constant calculation from double integrals a true identity?

A prime number is a number that is only divisible by itself and one, that is the number of divisors of a prime number is equal to $2$. One way to illustrate this is to plot a matrix such that if the ...
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### Limit of an equation similar to the Euler's constant definition

$$\lim_{n\to \infty} \left(2+\frac{1}{n}\right)^{n} = ?$$ I don't know even how to start this.
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### Use Euler's method with step size 10^-n to estimate x(1), where f(x) is the solution of the initial-value problem below. f(x)=-x x(0)=1

Use Euler's method with step size $10^{-n}$ for $n=1,2,3,4.$ to estimate $x(1)$, where $f(x)$ is the solution of the initial-value problem below. $x'=f(x)=-x$ $x(0)=1$ EDIT / UPDATE: x_n+1=x_n + ...
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### Potence of Euler's Number

Show with help of the Bernoulli Inequality that $$\lim_{n\rightarrow\infty}\left(1-\frac{1}{n^2}\right)^{n}=1$$ End with: $$\lim_{n\rightarrow\infty}\left(1-\frac{1}{n}\right)^n=\frac{1}{e}$$
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### Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication?

Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication? I had also got a clue: it's related to e. Please help! ...
While trying to prove integral with exponential function and logarithm in an alternative way, I came to this solution: $$\sum_{k=0}^{+\infty}(-1)^{k+1}\frac{\log (k+1)+\gamma }{(k+1)}.$$ As both ...