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Chapter 2: Derivatives

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Essential Calculus: Early Transcendentals
Pages: 73 - 144
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

292 Questions for Chapter 2: Derivatives

  1. A particle is moving along a hyperbola\(xy = 8\). As it reaches the point \(\left( {4,2} \right)\), the \(y{\rm{ - }}\)coordinate is decreasing at a rate of 3cm/s. How fast is the \(x{\rm{ - }}\)coordinate of the point changing at that instant?

    Found on Page 132

  2. Find \(\frac{{dy}}{{dx}}\) by the implicit differentiation.

    Found on Page 127

  3. Determine whether the statement is true or false. If it is true, explain

    Found on Page 140

  4. Verify the given linear approximation at \(a = 0\). Then determine the values of \(x\) for which the linear approximation is accurate to within \(0.1\).

    Found on Page 138

  5. Find the derivative of the function.

    Found on Page 120

  6. Find \({\rm{f'(x)}}\) from first principles, that is, directly from the definition of a derivative.

    Found on Page 141

  7. Find from first principles, that is, directly from the definition of a derivative. \({\rm{f(x)}} = {{\rm{x}}^{\rm{3}}} + {\rm{5x}} + {\rm{4}}\)

    Found on Page 141

  8. (a)What quantities are given in the problem?

    Found on Page 132

  9. Use a linear approximation (or differentials) to estimate the given number.

    Found on Page 139

  10. Find the derivative of the function.

    Found on Page 120

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