Posted by john on Friday, October 15, 2010 at 12:06am.
Please help !!!!!
Find dy/dx by implicit differentiation.
(sin πx + cos πy)4 = 65

calculus 1  drwls, Friday, October 15, 2010 at 6:04am
I assume that the 4 is an exponent, and you mean
(sin ðx + cos ðy)^4 = 65
Differentiate both sides of the equation with respect to x.
4 (sin ðx + cos ðy)^3 *d/dx[sin ðx + cos ðy] = 0
[sin(pi*x) + cos(pi*y)]^3 * [(pi*cos(pi*x)  pi*sin(pi*y)*(dy/dx)] = 0
You can divide out the first [ ] term on the left. Only second [] term can be zero.
(pi*cos(pi*x) = pi*sin(pi*y)*dy/dx
dy/dx = (1/pi)cot(pi*y) 
calculus 1  john, Friday, October 15, 2010 at 11:08am
(pi*cos(pi*x) = pi*sin(pi*y)*dy/dx
dy/dx = (1/pi)cot(pi*y)
I think the pi should be canceled, and the term cos and sin can not be identified as cot, because it is cos of x, and sin of y.
Is it right? 
calculus 1  drwls, Friday, October 15, 2010 at 12:06pm
pi can be cancelled, and yes, your are right about the cot.
Thank you for your alert corrections 
calculus 1  Matt, Friday, October 15, 2010 at 12:10pm
So, What do u think how we solve this? :)