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Derivative of cross-product of two vectors
In finding the derivative of the cross product of two vectors $\frac{d}{dt}[\vec{u(t)}\times \vec{v(t)}]$, is it possible to find the cross-product of the...
Apr 21, 2026
Archive: News
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Calculus question taking derivative to find horizontal tangent line
How would I solve this problem? Find the point where the tangent line is horizontal in the following function: $$f(x)=(x-2)(x^2-x-11)$$ I computed the der...
Apr 21, 2026
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Integrating $dS/S = \mu dt$
Integrating $dS/S = \mu dt$ between time $0$ and time $T$ we get $S_T = S_0e^{\mu T}$, for $S_0$ and $S_T$ stock prices at time $0$ and $T$. I'm tryi...
Apr 21, 2026
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Find dy/dx if y = .. and u = ..
I'm not absolutely sure on how I can deal with this problem with this problem: Find $ \dfrac{dy}{dx} $ if $ y = 2u^2 - 3u $ and $ u = 4x - 1 $ I am t...
Apr 21, 2026
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Find the marginal PMF of X given the following joint PMF
Oh boy, so this is a tough one. Let X and Y be 2 random variables with the joint pmf: $$p(x,y) = \frac{e^{-\lambda}\lambda^{x}p^{y}(1-p)^{x-y}}{y!(x-y)!}$...
Apr 21, 2026
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Example of tensor product of two representations
This is similar to what Serre wrote in his book on linear representations of finite groups by Serre: There is also the tensor product which has the proper...
Apr 21, 2026
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Derivative of $e^y=x^{\ln x}$?
How to obtain $y'$ from $e^{y}=x^{\ln x}$? This is what I did: $$\ln e^y = \ln x^{\ln x}$$ $$y = \ln ^2 x$$ $$y' = \frac{2 \ln x}{x}$$ Is this c...
Apr 21, 2026
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Differential calculus vs Integral calculus
I have never done integration in my life and I am in first year of university. Is it harder than taking the derivative? I've heard its just going bac...
Apr 21, 2026
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User Dylan Wilson - Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields
Apr 21, 2026
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Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$
Everyone knows about the classic $$ \sum_{i=1}^{\infty} \dfrac{1}{2^i} = 1 $$ However, is there any way to find $$ \sum_{i=0}^{\infty} \dfrac{1}{2^{2^i}} ...
Apr 21, 2026
