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Expert: Robi Bhattacharjee - 12/14/2008


Question
I need help implicitly differentiating cos(x+y) + sin (x-y) = 0 @ y' = (pi/4, -pi/4). There is something going on here that I'm not seeing. Is there a substitution that I need to make? Please help!!!


Answer
Hi Marcel,

Well, first of the point (pi/4, -pi/4) is not on the curve cos(x+y) + sin(x-y) = 0. Did you mean to type (-pi/4, pi/4)?

Assuming you did, hear goes.

cos(x+y) + sin(x-y) = 0

differentiating w.r.t.x we have

-sin(x+y)*(1 + dy/dx) + cos(x-y)*(1 - dy/dx) = 0

so dy/dx(sin(x+y) + cos(x-y)) = cos(x-y) - sin(x+y)

dy/dx = (cos(x-y) - sin(x+y))/((sin(x+y) + cos(x-y))

so at (-pi/4, pi/4) it = 0/0 which doesn't exit.

So the answer is DNE


I hope this helped,
Robi

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Robi Bhattacharjee

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I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

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I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

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I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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