3.3 Chain Ruleap Calculus

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3.3 Chain Ruleap Calculus 2nd Edition

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3.3 Chain Ruleap Calculus 14th Edition

This video explains about Topic 3.3 for subject BUM2123 Applied Calculus which will be used in Substitute Blended Learning. Unit 3: Trigonometry and the Chain Rule The chain rule is the most complex of the differentiation procedures. It is also the most powerful: with it you will be able to differentiate any algebraic function. By a trick of notation, it looks innocuous enough: Just cancel the du s. It should be stressed that this is a trick of the notation; the.

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. AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site.® is a trademark registered. Chain Rule appears everywhere in the world of differential calculus. Whenever we are finding the derivative of a function, be it a composite function or not, we are in fact using the Chain Rule. In this section, we will learn about the concept, the definition and the application of the Chain Rule, as well as a secret trick – 'The Bracket. More Lessons for Calculus Math Worksheets The Chain Rule The following figure gives the Chain Rule that is used to find the derivative of composite functions. Scroll down the page for more examples and solutions. In Leibniz notation, if y = f(u) and u = g(x) are both differentiable functions, then.

3.3 Chain Ruleap Calculus Calculator

Section 3-9 : Chain Rule

3.3 Chain Ruleap Calculus Solver

For problems 1 – 27 differentiate the given function.

  1. (fleft( x right) = {left( {6{x^2} + 7x} right)^4}) Solution
  2. (gleft( t right) = {left( {4{t^2} - 3t + 2} right)^{ - 2}}) Solution
  3. (y = sqrt[3]{{1 - 8z}}) Solution
  4. (Rleft( w right) = csc left( {7w} right)) Solution
  5. (Gleft( x right) = 2sin left( {3x + tan left( x right)} right)) Solution
  6. (hleft( u right) = tan left( {4 + 10u} right)) Solution
  7. (fleft( t right) = 5 + {{bf{e}}^{4t + {t^{,7}}}}) Solution
  8. (gleft( x right) = {{bf{e}}^{1 - cos left( x right)}}) Solution
  9. (Hleft( z right) = {2^{1 - 6z}}) Solution
  10. (uleft( t right) = {tan ^{ - 1}}left( {3t - 1} right)) Solution
  11. (Fleft( y right) = ln left( {1 - 5{y^2} + {y^3}} right)) Solution
  12. (Vleft( x right) = ln left( {sin left( x right) - cot left( x right)} right)) Solution
  13. (hleft( z right) = sin left( {{z^6}} right) + {sin ^6}left( z right)) Solution
  14. (Sleft( w right) = sqrt {7w} + {{bf{e}}^{ - w}}) Solution
  15. (gleft( z right) = 3{z^7} - sin left( {{z^2} + 6} right)) Solution
  16. (fleft( x right) = ln left( {sin left( x right)} right) - {left( {{x^4} - 3x} right)^{10}}) Solution
  17. (hleft( t right) = {t^6},sqrt {5{t^2} - t} ) Solution
  18. (qleft( t right) = {t^2}ln left( {{t^5}} right)) Solution
  19. (gleft( w right) = cos left( {3w} right)sec left( {1 - w} right)) Solution
  20. (displaystyle y = frac{{sin left( {3t} right)}}{{1 + {t^2}}}) Solution
  21. (displaystyle Kleft( x right) = frac{{1 + {{bf{e}}^{ - 2x}}}}{{x + tan left( {12x} right)}}) Solution
  22. (fleft( x right) = cos left( {{x^2}{{bf{e}}^x}} right)) Solution
  23. (z = sqrt {5x + tan left( {4x} right)} ) Solution
  24. (fleft( t right) = {left( {{{bf{e}}^{ - 6t}} + sin left( {2 - t} right)} right)^3}) Solution
  25. (gleft( x right) = {left( {ln left( {{x^2} + 1} right) - {{tan }^{ - 1}}left( {6x} right)} right)^{10}}) Solution
  26. (hleft( z right) = {tan ^4}left( {{z^2} + 1} right)) Solution
  27. (fleft( x right) = {left( {sqrt[3]{{12x}} + {{sin }^2}left( {3x} right)} right)^{ - 1}}) Solution
  28. Find the tangent line to (fleft( x right) = 4sqrt {2x} - 6{{bf{e}}^{2 - x}}) at (x = 2). Solution
  29. Determine where (Vleft( z right) = {z^4}{left( {2z - 8} right)^3}) is increasing and decreasing. Solution
  30. The position of an object is given by (sleft( t right) = sin left( {3t} right) - 2t + 4). Determine where in the interval (left[ {0,3} right]) the object is moving to the right and moving to the left. Solution
  31. Determine where (Aleft( t right) = {t^2}{{bf{e}}^{5 - t}}) is increasing and decreasing. Solution
  32. Determine where in the interval (left[ { - 1,20} right]) the function (fleft( x right) = ln left( {{x^4} + 20{x^3} + 100} right)) is increasing and decreasing. Solution