MAT.126 2.5-2.6

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MAT.126 2.5-2.6

2.6 Related Rates

Use related rates to solve real-life problems

Guidelines

Find a related rate

Differentiate implicitly wrt t

Use known equations

2.5 Implicit Differentiation

Use implicit differentiation to find the derivative of a function

Tangent Line to an Implicit Graph

Higher-Order Implicit Derivatives

Explicit Domains for Implicit Functions

Slope of an Implicit Graph

Graphing Implicit Relations

Process

Chain Rule

To differentiate an implicitly defined function one must use the chain rule on all terms involving y.

d dy

---[ f(y) ] = f'(y) ----

dx dx

Distinguish between functions written in implicit form and explicit form

Explicit: y = f(x)

Implicit: y and f(x) are mixed together