Question

Derive

y=6x^2 cosx cotx

Answer 1

Do you mean take the derivative with respect to x?

Answer 2

Yes

Answer 3

Remember your product rule?\[\large\rm (xy)'=x'y+xy'\]The rule follows the same pattern when you have three functions!\[\large\rm (xyz)'=x'yz+xy'z+xyz'\]

Answer 4

So your product rule set up would look like this,\[\large\rm \color{royalblue}{(6x^2)'}\cos x \cot x+6x^2\color{royalblue}{(cosx)'}cotx+6x^2 cosx\color{royalblue}{(cotx)'}\]Where the blue stuff is the derivatives you must take.

Answer 5

If you're not comfortable doing it this way,
you can instead rewrite cotx in terms of sines and cosines,
and then combine your cosine into the numerator,
and do product rule into quotient rule.

That seems like a big hassle though.

Answer 6

Oh I see. Thank you very much!