The question I'm having trouble with is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

Given that siny = 2sinx show that:

a) (dy/dx)^2 = 1+3sec^2(y), by differentiating this equation with respect to x show that

b)d^2y/dx^2 = 3sec^2ytany and hence that

c) coty(d^2y/dx^2) - (dy/dx)^2 + 1 = 0

Part (c) is straight forward and after a fair bit of work I got (a)...part (b) however is a *big* problem for me.

my favourite method of trying to solve the problem (because this question doesn't come anywhere close to the 4 examples the book has shown up to now) is to firstly to find the square root of both sides of the equation to get back to dy/dx and then differentiate working on the principle that this is the square root of a quotient.

dy/dx = sqrt(1+ 3sec^(2)y)...

(y'') = 1/2(y')(6cosysiny/cos^4(y))(1 + 3sec^2(y))^(1/2)...

(y'') = (y')(3sec^ytany)(1 + 3sec^2)^(1/2)

I am stuck here with the bit that I want nested within rubbish

can someone please show me what I should have done to reach the correct answer?

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# Homework Help: Another implicit differentiation Problem

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