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- Calculus 1
- Differentiation
Chain rule
- Intro Lesson24:16
- Lesson: 16:41
- Lesson: 2a7:01
- Lesson: 2b8:53
- Lesson: 3a6:39
- Lesson: 3b6:28
- Lesson: 3c10:02
- Lesson: 3d14:58
- Lesson: 3e5:45
- Lesson: 4a12:24
- Lesson: 4b15:33
- Lesson: 4c10:41
- Lesson: 5a2:22
- Lesson: 5b6:56
- Lesson: 5c3:57
- Lesson: 5d10:29
- Lesson: 6a11:38
- Lesson: 6b5:18
Chain rule
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 Technique".
Lessons
Chain Rule
if: y=f()
then: dxdy=f′()⋅dxd()
Differential Rules
if: y=f()
then: dxdy=f′()⋅dxd()
Differential Rules


- IntroductionIntroduction to Chain Rule
• "bracket technique" explained!
• exercise: dxdx10 VS. dxd(x5+4x3−6x+8)10 - 1.Differentiate: Polynomial Functions
dxd(2x−1)3 - 2.Differentiate: Rational Functionsa)dxd(4x3+7)101b)dxd−sin2x5
- 3.Differentiate: Radical Functionsa)dxdx3+4x2−9b)dxd3(x2+5)7c)dxd36x4−x1d)dxdx+x+xe)dxd3lnx
- 4.Differentiate: Trigonometric Functionsa)Differentiate: y=sin4x VS. y=sin(x4)b)dxdtan(cose5x2)c)dθdsin(cos(tanθ))
- 5.Differentiate: Exponential Functionsa)dxdetanxb)dxdecsc5x2c)dxd2sinxd)dxd52x3
- 6.Differentiate: Logarithmic Functionsa)dxdlnx100 VS. dxd(lnx)100b)dxdlog2x3
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2.
Differentiation
2.1
Definition of derivative
2.2
Estimating derivatives from a table
2.3
Power rule
2.4
Slope and equation of tangent line
2.5
Chain rule
2.6
Derivative of trigonometric functions
2.7
Derivative of exponential functions
2.8
Product rule
2.9
Quotient rule
2.10
Implicit differentiation
2.11
Derivative of inverse trigonometric functions
2.12
Derivative of logarithmic functions
2.13
Higher order derivatives