Implicit differentiation is a helpful method we use when we have equations with both (x) and (y) that are hard to solve for (y).
Instead of trying to get (y) all by itself, we take the derivative of both sides of the equation with respect to (x). We treat (y) as if it depends on (x) and use something called the chain rule.
Why It’s Important:
More Flexible: It works well with complicated relationships.
Saves Time: You don’t have to solve for (y) first.
Better Understanding: It helps us gain more insight into curves and shapes.
Using implicit differentiation helps us dive deeper into calculus and understand its uses better, especially with related rates and sketching curves!
Implicit differentiation is a helpful method we use when we have equations with both (x) and (y) that are hard to solve for (y).
Instead of trying to get (y) all by itself, we take the derivative of both sides of the equation with respect to (x). We treat (y) as if it depends on (x) and use something called the chain rule.
Why It’s Important:
More Flexible: It works well with complicated relationships.
Saves Time: You don’t have to solve for (y) first.
Better Understanding: It helps us gain more insight into curves and shapes.
Using implicit differentiation helps us dive deeper into calculus and understand its uses better, especially with related rates and sketching curves!