# 3.3 Chain Ruleap Calculus

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### 3.3 Chain Ruleap Calculus 2nd Edition Show All Notes  Hide All Notes ### 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 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{{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{{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