# How do you implicitly differentiate #7=1-(y-x)/y^2#?

##### 1 Answer

Nov 12, 2016

# dy/dx = 1/(1+12y) #

#### Explanation:

The equation does not express

# g(y) = f(x) #

# :. d/dx g(y) = d/dx f(x) #

# :. dy/dx d/dy g(y) = f'(x) #

# :. g'(y) dy/dx= f'(x) #

So for

# -6 = (y-x)/y^2#

# :. -6y^2 = y-x #

# :. -12ydy/dx = dy/dx-1 #

# :. dy/dx+12ydy/dx = 1 #

# :. (1+12y)dy/dx = 1 #

# :. dy/dx = 1/(1+12y) #