Question

Please help !!!!!
Find dy/dx by implicit differentiation.
(sin πx + cos πy)4 = 65

Answer 1

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)

Answer 2

(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?

Answer 3

pi can be cancelled, and yes, your are right about the cot.
Thank you for your alert corrections

Answer 4

So, What do u think how we solve this? :)