Question

derivative of trig functions

Answer 1

@zepdrix the answer in the box is what i got

Answer 2

\[\Large h(t)=23\csc t+t \cot t\]So... product rule on the second term, yes?
\[\Large h'(t)=23\color{royalblue}{(\csc t)'}+\color{royalblue}{(t)'}\cot t+t \color{royalblue}{(\cot t)'}\]

Answer 3

hmm im trying to understand..

Answer 4

okay so it would be -23 csc t*cot t+ 1*cot t +t -csc^2 t

Answer 5

is that correct @zepdrix i know looks really confusing

Answer 6

yes looks good.
But please please please, try to get used to using brackets.

This part here is really sloppy, it looks like subtraction: t -csc^2 t
where as it's suppsed to be multiplication which is what I'm sure you meant to write.
t(-csc^2 t)

Answer 7

yes im sorry its just putting the brackets on this website is very confusing

Answer 8

hah :3 fair enough

Answer 9

i have a question how come we didnt use the product rule for 23 csc t?

Answer 10

There is only one function of t within that term, namely csc t.

Are you asking because of the 23 in front? Or just because you thought we might have to based on the fact that we used product rule in the other place?

Answer 11

no because of the 23 in the front

Answer 12

is it because its a constant?

Answer 13

yes :) constants don't affect the differentiation process.
We can ignore them when we take a derivative.\[\Large (23\csc t)'\quad=\quad 23(\csc t)' \quad=\quad 23(-\csc t \cot t)\]

Answer 14

okay got it! thank you so much. you're a very big help

Answer 15

yay team \c:/