Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter

    Ive got a question that I just can't seem to get the answer to:
    find dy/dx of  \sqrt {xy} + \sin x + \cos y = 0

    The final answer is  \frac{y + 2 \sqrt { \cos x }} {2 \sqrt {xy}  \sin y - x} but I am not entirely sure on how to get to this stage.

    My attempt:
    I think I worked the derivative of
     \sqrt {xy} to be  \frac{1}{2 \sqrt {xy}} * (y + x * \frac{dy}{dx})
    The derivative of
     \sin x to be  cosx (obviously)
    And finally
     \cos y to be  (- \sin y \frac{dy}{dx})

    Move the sin(x) term to the RHS (it`s easier to deal then with factorising the y ' (x) terms)

    differentiate the entire thing, so you get:

    \displaystyle  \frac{y^{1/2}}{2x^{1/2}}+\frac{x^{1/2}}{2y^{1/2}}y'- \sin(y) y ' = -\cos(x)

    then multiply the entire equation by:


    and see where that gets you..

    (ooh, and factor out the y' on the LHS, moving the 1st term in the 1st line above to the RHS)

    • Thread Starter

    I've tried it again, using methods that you showed and have ended up with (-y-2cos(x)(xy)^1/2) / (-2((xy)^1/2) sin(y)-x)
    Apologies, LaTex isn't working for some reason.

    your answer is correct apart from a minus sign infront of 2root(x)root(y) in the denominator (maybe a small mistake somewhere) - just take a factor of -1 out from the numerator in the answer you gave, THEIR numerator is incorrect as it doesn`t have the root(xy) term (the root(cos(x) term is wrong also)
    • Thread Starter

    That's how I'll deal with all problems in the future. If my answer doesn't match theirs, their answer is wrong! :P But seriously, I think you're right, I see no possible way of getting root cos anywhere in that equation. Thanks for the help!
Submit reply
Turn on thread page Beta
Updated: January 28, 2015
Are you going to a festival?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.