If you could just get me off to a good start I would really appreciate it. Thanks!
2006-09-12 15:47:56 · 2 answers · asked by cheezo12 1 in Science & Mathematics ➔ Mathematics
d/dx(sinx*cosy) = d/dx(y^2)
sinx * d/dx(cosy) + cosy * d/dx(sinx) = 2y * dy/dx
sinx * -siny * dy/dx + cosy * cosx = 2y * dy/dx
From algebra...
dy/dx = (cosx * cosy)/(2y + sinx * siny)
My answer is sound, remember y is a function of x, NOT INDEPENDENT OF X, and use implicit differentiation! Furthermore if y^2=sinx cosy you can not assume that y = sqrt(sinx*cosy) when clearly also y = -sqrt(sinx*cosy) satisfies the relation. Also, how exactly are you "solving for y" when y still remains on both sides of the equation? Fortunately it's not necessary to do so.
2006-09-12 16:01:16 · answer #1 · answered by Andy S 6 · 2⤊ 1⤋
Andy is right: you do need to use implicit differentiation.
2006-09-12 17:13:37 · answer #2 · answered by Jimbo 5 · 0⤊ 1⤋