The derivatives of: $$\frac{d}{dx}\sin(x)=\cos(x)$$ $$\frac{d}{dx}\cos(x)=-\sin(x)$$ I currently trying to teach a friend of mine calculus, because he does not know it yet. He keeps forgetting how to take the derivatives of $\sin(x)$ and $\cos(x)$. Is there a simple way, or trick to remember the derivatives of $\sin(x)$ and $\cos(x)$?

Is it possible in some cases that using the ILATE rule does not yield an explicit antiderivative but making another choice does yields one? If so, please give examples.

Sometimes formulas in linear algebra are not easy to remember. Some usefulness for the process of remembering can provide application of mnemonics. Do you know some useful mnemonics for this purpose? I’ll give two examples: For the process of finding the inverse of matrix it could be used mnemonic Detminstra what can be translated as […]

Please how can I easily remember the following trig identities: $$ \sin(\;\pi-x)=\phantom{-}\sin x\quad \color{red}{\text{ and }}\quad \cos(\;\pi-x)=-\cos x\\ \sin(\;\pi+x)=-\sin x\quad \color{red}{\text{ and }}\quad \cos(\;\pi+x)=-\cos x\\ \sin(\frac\pi2-x)=\phantom{-}\cos x\quad \color{red}{\text{ and }}\quad \cos(\frac\pi2-x)=\phantom{-}\sin x\\[12pt] \text{and similar things where we add a radian angle inside cos or sin as you can see} $$ So how can I remember […]

For a sequence of non-negative measurable functions $f_n$, Fatou’s lemma is a statement about the inequality $$\int \liminf_{n\rightarrow \infty} f_n \mathrm{d}\mu \leq \liminf_{n\rightarrow \infty}(\int f_n \mathrm{d} \mu)$$ or alternatively (for sequences of real functions dominated by some integrable function) $$\limsup_{n\rightarrow \infty}(\int f_n \mathrm{d} \mu) \leq \int \limsup_{n\rightarrow \infty} f_n \mathrm{d}\mu$$ I keep forgetting the direction […]

My math professor recently told us that she wants us to be familiar with summation notation. She says we have to have it mastered because we are starting integration next week. She gave us a bunch of formulas to memorize. I know I can simply memorize the list, but I am wondering if there is […]

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