It is unlikely that the result of distributing then differentiation will result in something that is accepted. The difference between "not the simplest" and that is an ocean.

But multiple answers are likely correct, because this is a trigonometric expression. There are many equivalent, equally simple ways to represent many such expressions. Makes grading quite difficult. Just because you've never seen or even conceived of an answer does not automatically make it wrong.

I only suggested that as the next step... not the end result.

The next step is far easier if you apply the product rule, rather than going to the basic principles of distributing, differentiating, and factoring.

Applying the product rule leaves the result partially factored. That's why it is used.

Thank you for the correction. I lost track there.

I've, uh, done a bit of calculus in my day.

there is a mistake here. Either your substitution or diff'ing missed something.

the derivative of theta wrt theta is 1. So in these parentheses you should get a -1 and +1...they cancel

my final was y'= -@*cos@/sin^2@ - 2*cos^2@/sin^3@

I can show algebra if you need it.. just lazy right now.

do you have Maple?

It makes you a better person.

I'm sure Buddha or Lao-Tzu would agree.

it isn't really a mistake.. just a poor choice.

I think you have something equivalent... but keep the cot form and you should be able to put your two 'sides' together.

well the form is gf'+fg'

-csc^2@ is the differention of cot@

Have you tried www.wolframalpa.com dont forget to click on show steps

__________________
Grumpy Old Diesel Owners Club group

I no longer question authority, I annoy authority. More effect, less effort....

1967 230-6 auto parts car. rust bucket.
1980 300D now parts car 800k miles
1984 300D 500k miles
1987 250td 160k miles English import
2001 jeep turbo diesel 130k miles
1998 jeep tdi ~ followed me home. Needs a turbo.
1968 Ford F750 truck. 6-354 diesel conversion.
Other toys ~J.D.,Cat & GM ~ mainly earth moving

This is the Wiley Plus online math stuff is it? Just curious.

Also, what major are you again? I took a pre-calc/trig course that I should not have...I regret it. A LOT.

__________________

y=csc@*(@+cot@)

y'=-@*csc@cot@*(@+cot@)+csc@*[1+(-1-cot^2@)]

=-@*1/sin@*1/tan@ - 2/(sin@*tan^2@)

=-@*cos@/sin^2@ - 2*cos^2@/sin^3@

wolframalpha. com


confusing if you can't do it by hand first.

its great for checking answers, not for doing algebra.

remember the identity you gave in the earlier post?

use that to give each 'side' a cot function. This will allow you to combine them.

I also checked that answer I supplied with software

here is a link to layback's suggestion

it shows some other variations