# 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 #