Question

what is the derivative of this respect to x

1- 4 * 100 *1*[(cos((pi/6)-x)-cos(pi/6)]*tan((pi/6)-x)

Answer 1

i assume this is part of some larger problem, because you don't usually see \(1-4\times 100\times 1\)

Answer 2

it looks like the whole thing is
\[1-400(\cos(\frac{\pi}{6}-x)-\cos(\frac{\pi}{6}))\tan(\frac{\pi}{6}-x)\] multiply out first

Answer 3

you are going to end up with \[1-400\sin(\frac{\pi}{6}-x)+200\tan(\frac{\pi}{6}-x)\] then take the derivative of that

Answer 4

ok looking good

Answer 5

derivative of \(\sin(\frac{\pi}{6}-x)\) is \(-\cos(\frac{\pi}{6}-x)\) by the chain rule etc. you could also use the "subtraction angle formula" if you wanted to rewrite \(\sin(\frac{\pi}{6}-x)=-\sin(x-\frac{\pi}{6})=\frac{1}{2}\cos(x)-\frac{\sqrt{3}}{2}\sin(x)\)
and then differentiate that one.
you have a lot of constants to keep track of so be careful