Sometimes we come across equations that do not isolate y. Until now, we did not know how to take the derivative of these equations. Until, we learned about implicit differentiation. To use implicit differentiation, multiply by the derivative of y with respect to x each time you differentiate an expression containing y. Then, solve for the derivative of y with respect to x. Essentially what you are doing is treating y as an entirely separate function. This sounds a little confusing, but let’s work it out with an example.
How to solve implicit problems:
1. Rewrite the expression with all y’s in parenthesis.
2. Differentiate the expression with respect to x.
3. If the problem is asking for the slope of dy/dx, solve for dy/dx.
4. If the problem is asking for the equation of a tangent line, use your point and derivative to find the y- intercept.
Examples of differentiation:
How to solve implicit problems:
1. Rewrite the expression with all y’s in parenthesis.
2. Differentiate the expression with respect to x.
3. If the problem is asking for the slope of dy/dx, solve for dy/dx.
4. If the problem is asking for the equation of a tangent line, use your point and derivative to find the y- intercept.
Examples of differentiation: