Determine the Desired Derivative

• Set up the equation and determine the dependent and the independent variable. Then determine the desired derivative form (whether it is dy/dx, dx/dy, or some other form).
  
  

Differentiate Each Term

• Use the chain rule and any other necessary rules (e.g, power rule, quotient rule, product rule, trigonometric rules for differentiation) to differentiate each term in the entire equation. Find the d/dx of each term under the chain rule. For example, if the equation is (x^2) + (y^2) = 25, do the following: d/dx ( (x^2) + (y^2) = 25 ).
  
  

Simplify

• Simplifying the aforementioned equation results in d/dx (x^2) + d/dx (y^2) = d/dx (25), which is the same as (2x) + (2y) (dy/dx) = 0.
  
  

Rearrange and Solve for Derivative

• The final step is to solve for dy/dx by rearranging the terms. So, it would result in (2y) (dy/dx) = -2x, and then dy/dx = -2x/2y = -x/y.