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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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17.
Derivatives
17.1
Definition of derivative
17.2
Power rule
17.3
Gradient and equation of tangent line
17.4
Chain rule
17.5
Derivative of trigonometric functions
17.6
Derivative of exponential functions
17.7
Product rule
17.8
Quotient rule
17.9
Implicit differentiation
17.10
Derivative of inverse trigonometric functions
17.11
Derivative of logarithmic functions
17.12
Higher order derivatives