Given that # sin(x/y) = 1/2 # find #dy/dx#?
1 Answer
Nov 1, 2017
# dy/dx = y/x #
Explanation:
We have:
# sin(x/y) = 1/2 #
Differentiating Implicitly wrt
# \ \ \ \ cos(x/y) {d/dx(x/y)} = 0 #
# :. cos(x/y) { (y)(d/dx x) - (d/dx y)(x) } / (y)^2 = 0 #
# :. cos(x/y) { (y)(1) - (dy/dx)(x) } / y^2 = 0 #
# :. cos(x/y) { y - x dy/dx } / y^2 = 0 #
# :. y - x dy/dx = 0 #
# :. x dy/dx = y #
# :. dy/dx = y/x #
