AP®MathsCollege BoardCalculus ABExam QuestionsUnit 3: Differentiation of Composite, Implicit & Inverse FunctionsImplicit Differentiation

Implicit Differentiation (College Board AP® Calculus AB)

Exam Questions

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Implicit Differentiation

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Implicit Differentiation

1
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If x equals sin space y then fraction numerator d y over denominator d x end fraction equals

  • fraction numerator negative 1 over denominator square root of 1 minus x squared end root end fraction

  • fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction

  • fraction numerator 1 over denominator cos space x end fraction

  • fraction numerator 1 over denominator 1 minus x squared end fraction

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2
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If negative 3 x squared plus 2 x y equals 12, then when x equals 1, fraction numerator d y over denominator d x end fraction equals

  • negative 9 over 2

  • 9 over 2

  • 15 over 2

  • negative 15 over 2

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3
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If the equation of a curve is 2 x minus 4 x y plus 2 y squared equals 4, then at the point (2, 4), fraction numerator d y over denominator d x end fraction is

  • negative 7 over 4

  • 7 over 4

  • 1 fourth

  • negative 11 over 8

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4
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fraction numerator d over denominator d x end fraction open parentheses 2 x to the power of ln space x end exponent close parentheses equals

  • 2 over x open parentheses ln space x close parentheses open parentheses x to the power of ln space x end exponent close parentheses

  • 2 x to the power of ln space x end exponent

  • 4 over x open parentheses ln space x close parentheses open parentheses x to the power of ln space x end exponent close parentheses

  • 4 x to the power of ln space x end exponent open parentheses ln space x close parentheses

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51 mark

If x to the power of 4 minus 6 x y squared plus 9 y equals 10, then fraction numerator d y over denominator d x end fraction equals

  • fraction numerator 4 x cubed minus 6 y squared over denominator 12 x y plus 9 end fraction

  • fraction numerator 4 x cubed minus 6 y squared over denominator 12 x y minus 9 end fraction

  • fraction numerator 4 x cubed minus 6 y squared plus 9 over denominator 12 x y end fraction

  • fraction numerator 4 x cubed minus 12 x y minus 6 y squared over denominator 9 end fraction

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