Integration 2 elur niahc
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1) The document discusses how to integrate composite functions using the chain rule. It provides the example of integrating y = (7x + 2)5 by letting u = 7x + 2 and then applying the chain rule. 2) The document also discusses the general rule for integrating expressions of the form (ax + b)n, which is (ax + b)n+1 / (n+1)a + c. It provides several examples of using this rule. 3) The examples shown integrate expressions including (5x + 7)3, (9x + 3)6, (5 - 4x)7, and 4(5 - 3x)5. The document emphasizes setting up
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Are miscommunications, handoff delays and unforeseen issues impacting your organization's ability to deliver? View these slides to learn how to reflect your work structure in LeanKit so that you can keep work flowing across multiple teams.
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1) The document explains the chain rule for differentiating composite functions.
2) It provides examples of applying the chain rule to functions of the form f(g(x)) where f and g are different functions.
3) The key steps are to let the inner function g(x) equal a variable u, take the derivative of the outer function f(u) with respect to u, and multiply it by the derivative of the inner function g(x) with respect to x.
Chain rule
The chain rule allows you to take the derivative of a composite function f(g(x)). It states that the derivative of f(g(x)) is f'(g(x)) * g'(x). You apply the chain rule by taking the derivative of the outside function first, and then taking the derivative of the inside function. The chain rule can also be used with the product rule and quotient rule when differentiating composite functions.
Chain rule
The chain rule allows you to take the derivative of a composite function f(g(x)). It states that the derivative of f(g(x)) is f'(g(x)) * g'(x). You apply the chain rule by taking the derivative of the outside function first, then taking the derivative of the inside function. The chain rule can also be used with the product rule and quotient rule when differentiating composite functions.
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Pt 2 turunan fungsi eksponen, logaritma, implisit dan cyclometri-d4
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2. Several examples are worked through, applying the formulas to find the derivatives of functions like y = ecos5x, y = (e4x - e5x)4, and implicit functions like x3 + y4 = 0.
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This document contains examples of operations with exponents (powers) such as:
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Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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Integration 2 elur niahc
- 2. What is to be learned? • How to integrate composite functions
- 3. y = (7x + 2)5 let y= u5 where u = 7x + 2 dy /du = 5u4 du /dx = 7 dy /du du /dx dy /dx = dy /dx = 5u4 7 =5(7x + 2)4 7 Add 1 to power Chain Rule
- 4. y = (7x + 2)5 let y= u5 where u = 7x + 2 dy /du = 5u4 du /dx = 7 dy /du du /dx dy /dx = dy /dx = 5u4 7 Chain Rule =5(7x + 2)4 7 ÷ 5 Add 1 to power
- 5. y = (7x + 2)5 let y= u5 where u = 7x + 2 dy /du = 5u4 du /dx = 7 dy /du du /dx dy /dx = dy /dx = 5u4 7 =5(7x + 2)4 7 ÷ 5 ÷ 7 Add 1 to power Chain Rule
- 6. ∫ (ax + b)n = (ax + b)n+1 (n+1)a Elur Niahc∫ (ax + b)n ∫ (5x + 7)3 dx dx = (5x + 7)4 (4)5 = (5x + 7)4 20 + c
- 7. ∫ (9x + 3)6 dx = (9x + 3)7 (7)9 = (9x + 3)7 63 + c ∫ (5 – 4x)7 dx = (5 – 4x)8 (8)-4 = (5 – 4x)8 32 + c-
- 8. ∫ 4(5 – 3x)5 dx = 4(5 – 3x)6 (6)-3 = 4(5 – 3x)6 -18 + c = 2(5 – 3x)6 9 + c-
- 9. ∫ (ax + b)n = (ax + b)n+1 (n+1)a Elur Niahc ∫ (ax + b)n ∫ (3x + 8)6 dx dx = (3x + 8)7 (7)3 = (3x + 8)7 21 + c Integration 2 + c
- 10. ∫ 3(5 – 6x)8 dx = 3(5 – 6x)9 (9)-6 = 3(5 – 6x)8 -54 + c Key Question = - (5 – 6x)8 18 + c