Please help my niece, below:

Given that x^2tany=9

Show that dy/dx=-18/x^4+81

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Well, I can tell her that the debit is the side nearest the window, if that helps.

Definitely a level question if both sides are equal

42

Is there a fake tan in the top equation?

Start there.

You may derive some solace, at a tangible level.

Share your solution in the light of the above.

Show your workings, to gain brownie points.

Ignore secants, cosines.

Answer by return please.

This site never ceases to amaze me ... even if possibly unintentionally.

It's over 50 years since my Maths A level (and indeed subsequent S level), but I really enjoyed that YouTube clip (not a phrase readily enunciated by me)!

Thanks.

I didn’t get that exactly unless you are missing an x but it has been 30 years since A level maths.

tany=9x^-2

sec^2y=1+tan^2y

sec^2y=1+81x^-4

sec^2ydy/dx=-18x^-3

dy/dx=-18x^-3/((1+81x^-4)=-18x/(x^4+81)

Purely out of curiosity (and given the sensitivity of some members of this site on the topic) ...

* Why did you initially post anonymously?

* Why are you now happy to break that anonymity?

Basically, were those both conscious decisions? Or, despite what we're told, did you find a way to make that initial selection accidently? I'm really interested.

Any idea about what I asked !

Oh it was you, was it?

It may surprise you but accountants don't need much arithmetic beyond add, take away, timesing and sharing. Newtonian calculus isn't part of our day to day life.

Hence the light hearted good natured chaffing in the replies.

Is about my niece, dont you get it?

If you dont know, please dont bla bla

You're asking in the wrong place.

Why are you asking accountants about differential calculus?

Try www.differential calculus.net

Plenty, but you'd already received some good assistance - which considering that the OP was wholly irrelevant to accounting matters I think was extremely kind of the responders.

Why are you behaving in quite the opposite manner, when a perfectly polite (and relevant) question is asked of you?

[I went to great pains to make it clear that I was honestly interested in the facts and not having a dig at you ... which frankly I'm now beginning to regret].

There must be a mathematical equation for this ...

Well it's a bit simplistic, but 'Regret (decision theory)' states that:

"when making decisions under uncertainty—should information about the best course of action arrive after taking a fixed decision—the human emotional response of regret is often experienced, and can be measured as the value of difference between a made decision and the optimal decision."

There's always an equation of some sort (more truly often a formula) for every situation! : -)

dx/dy = -18/x^4+81

There, I’ve shown you.

I gave you the proof and you said my answer was right even though you had missed an x in your post.

She needs to go back to her notes or speak to her teacher if she doesn’t understand the proof (which bit as I did it all for her?!).

When I help my daughter with her Maths we start with what she has been taught in class.

There must be other sites which can help, why did you post on here anyway? And please be nice as I spent an hour on this yesterday.

Matrix has given you.the stepping stones. There's some workings between lines 3 and 4 that Matrix has done offscreen, but your niece should be able to replicate them. Divide one side by tany and the other by tany expressed as a function of x (as given in the question).

Actually that's an alternative proof.

Matrix's (I now realise) is far simpler - just differentiate the original equation wrt x.

All double dutch to me.