Math Problem Statement
Given xy+2x+3x2=9: (a) Find y′ by implicit differentiation (leave your answer in terms of x and y). (b) Solve the equation for y and differentiate to get y′ in terms of x. (The answers should be consistent!)
(a) y′=
(b) y′=
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Algebra
Quotient Rule
Differentiation
Formulas
Product rule: (uv)' = u'v + uv'
Quotient rule: (u/v)' = (v * u' - u * v') / v^2
Theorems
Chain Rule
Product Rule
Quotient Rule
Suitable Grade Level
Grades 11-12