4.5 Implicit Differentiation.pptx - MATH 12 4.5 Implicit Differentiatio n Try differentiating Lesson Objective By the end of the lesson I will be able

# 4.5 Implicit Differentiation.pptx - MATH 12 4.5 Implicit...

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4.5 Implicit Differentiatio n Try differentiating 10/29/19 MATH 12
Lesson Objective By the end of the lesson, I will be able to… compute the derivative of an implicit function
Explicit vs. Implicit Functions An explicit function is an equation where the variable is explicitly written as a function of . E.g. An implicit function is an equation where neither variable has been (or cannot be) isolated . E.g.
Deriving Implicit Functions? Consider when you can isolate for … E.g. Differentiate What if you cannot isolate for ? E.g. Differentiate
Implicit Differentiation To find implicitly , we must apply differentiation with respect to x . If this involves just , differentiate as normal However involving , you must apply the chain rule because is defined implicitly as a differentiable function of .
Ex1. Differentiating with Respect to a) b) c) d)
Guidelines for Implicit Differentiation (p302) 1)Differentiate both sides of the equation with respect to2)Collect all terms of to the left side3)Factor4)Solve for
Ex2. Implicit Differentiation Solve for … a) b) c)
Ex3. Find the slope of the tangent to the curve…at (0, -2)
Ex4. Find of ( ? + ? ) 3 = 8 ?
Lesson Objective By the end of the lesson, I will be able to… compute the derivative of an implicit function
Suggested Practice Read pg 302 – Guidelines for Implicit Differentiation Page 306 #1-9,15,19,25,27,29,35,37 (odd #s ) Vocabulary: Explicit function, implicit function, implicit differentiation