However, some equations are defined implicitly by a relation between x and y.
For example:
x2 + y2 = 16
x2 + y2 = 4xy
We do not need to solve an equation for y in terms of x in order to find the derivative of y. Instead, we can use the method of implicit differentiation. This involves differentiating both sides of the equation with respect to x and then solving the resulting equation for y'.
Example:
If x2 + y2 = 16, find
Solution:
Step 1: Differentiate both sides of the equation
Step 2: Using the Chain Rule, we find that
Step 3: Substitute equation (2) into equation (1)
Step 4: Solve for
Example:
Find y’ if x3 + y3 = 6xy
Solution:
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.