Memorizing Formulas for Differentiation Once upon a time, I memorized the following formula out of laziness. 
Let $k(x)=\frac{f(x)^{g(x)}h(x)+i(x)}{j(x)}$. Then $k'(x)$ is as follows. 
$k'(x)=\frac{j(x)(g(x)h(x)f(x)^{g(x)-1}f'(x)+f(x)^{g(x)}(h(x)log(f(x))g'(x)+h'(x)+i'(x))-j'(x)(h(x)f(x)^{g(x)}+i(x))}{j(x)^2}$
(as confirmed by wolframalpha)
This was because I did not want to bother with logarithmic functions or the chain rule to find the derivatives of functions such as $x^{sin(x)}$
After some considerable time and effort, I had managed to memorize the formula. 
However, I had trouble actually applying this formula to tests for $f'(x)$, mostly because the formula is too long and complicated, and started to wonder if I had wasted my time and effort. 
This suspicions were heightened when I made several mistakes while using this formula. 
Would memorizing such a formula actually prove useful for tests?
Any advice would be appreciated. 
 A: As already said in comments, it does not seem useful at all to memorize this. Using it does not prove that you know how to make it and there so many  more important things to memorize in mathematics !
Let us do it simple $$k(x)=\frac{f(x)^{g(x)}h(x)+i(x)}{j(x)}=\frac{u(x)}{j(x)}$$ $$k'(x)=\frac{u'(x)j(x)-u(x)j'(x)}{j^2(x)}$$ $$u(x)=f(x)^{g(x)}h(x)+i(x)=t(x)h(x)+i(x)\implies u'(x)=t'(x)h(x)+t(x)h'(x)+i'(x)$$ $$t(x)=f(x)^{g(x)}\implies \log(t(x))=g(x)\log(f(x))$$ $$\frac{t'(x)}{t(x)}=g'(x)\log (f(x)) +g(x)\frac{ f'(x)}{f(x)}$$
By the way, if you had to program $k'(x)$ given the different functions $f(x)$, $g(x)$, $h(x)$, $i(x)$, $j(x)$, would you code the monster or just use pieces in the spirit of what I wrote ? 
A: Memorizing the formula is not much useful according to me.
Instead, I would say, memorize the formula for chain rule and apply it to derive the formula in the exam. It is true that sometimes it might take more time, but it is sure to work and doesn't go wrong. Also, the problem will be quite simplified sometimes when you start by the fundamentals. I took many reputed tests and I speak from the experience ( I wrote IITJEE-2012 and CAT-2016 in India, and got 150-odd national rank in both ,if you know what I mean)
