Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

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Presentation transcript:

Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

Implicit Differentiation

OK, here is how I like to attack these :

Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative

Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative

Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative - get the y’s together and take the derivative

Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative - get the y’s together and take the derivative

Implicit Differentiation

this is the derivative

Implicit Differentiation

Let’s get it in standard form :

Implicit Differentiation Let’s get it in standard form :

Implicit Differentiation Let’s get it in standard form : - get your x’s and number together and take the derivative

Implicit Differentiation Let’s get it in standard form : - get your y’s together and take the derivative

Implicit Differentiation Let’s get it in standard form :

Implicit Differentiation Let’s get it in standard form :

Implicit Differentiation Let’s get it in standard form :

Implicit Differentiation Let’s get it in standard form :

Implicit Differentiation Let’s get it in standard form : - This is your derivative

Implicit Differentiation

- Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

Implicit Differentiation - Use a and b again like we did with complex functions and the product rule… - When you can, you should simplify as far as possible…

Implicit Differentiation

- again, you should simplify as far as possible…

Implicit Differentiation Now substitute your ( - 5, 17 ) into your derivative to find the slope of the tangent line…