U3 Cn4 Implicit Differentiation
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Implicit differentiation is a technique used to find derivatives of functions that cannot be solved explicitly for y. It involves taking the derivative of the entire function using the chain rule, treating y as a variable rather than a function of x. This results in an expression for dy/dx that can be solved algebraically. Like other derivatives, dy/dx gives the slope of the tangent line at a point (x,y) on the curve, and this slope can be used along with the point to find the equation of the tangent line.
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U3 Cn4 Implicit Differentiation
- 1. Implicit Differentiation Unit 3 Lesson 4 Potomac School E. Alexander Burt
- 2. When to use Implicit Differentiation When you have a function that cannot be solved explicitly for y
- 3. Examples:
- 4. The method, part 1: Since we cannot solve for y, we must treat y as an unknown function of x
- 5. Therefore, the derivative of y follows the chain rule:
- 6. Method, part deux Take the derivative of the function, treating y as an unknown function of x
- 7. Solve algebraically for dy/dx
- 8. Tangent Lines Like any other derivative, dy/dx is the slope of a line tangent to the curve at (x,y)
- 9. Unlike previous functions, it can be difficult to find y if you are only given x
- 10. Usually, you will be given both x and y
- 11. The procedure is the same as it ever was: Use the derivative to find a slope, and with the point and the slope, write the equation of the line.