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- Calculus 1
- Differentiation
Higher order derivatives
- Intro Lesson2:17
- Lesson: 1a2:05
- Lesson: 1b2:01
- Lesson: 1c14:14
- Lesson: 1d0:48
- Lesson: 1e1:50
- Lesson: 2a7:48
- Lesson: 2b3:40
- Lesson: 3a4:08
- Lesson: 3b4:03
Higher order derivatives
Basic Concepts: Power rule, Chain rule, Derivative of exponential functions, Implicit differentiation
Lessons
Note
If f′(x) is the derivative of f(x), then we say that f"(x) is the 2nd derivative of f(x). Similarly, f(n)(x) is the n′th derivative of f(x).
If f′(x) is the derivative of f(x), then we say that f"(x) is the 2nd derivative of f(x). Similarly, f(n)(x) is the n′th derivative of f(x).
- IntroductionThe concept of higher order derivatives
- 1.1st and 2nd derivatives.
Find the first and second derivative for the following functions:
a)f(x)=x4+5x2+3x+2b)f(t)=sin(2t)c)g(s)=(2s+5s2)7d)y=5e)f(x)=5lnx - 2.2nd derivatives with implicit differentation
Find y" by implicit differentiation for the following functions:a)x2+y2=9b)x2+xy=9 - 3.Derivatives with repeating patterns
Find f(100)(x) for the following functions:a)f(x)=sin(x)b)f(x)=e(2x)
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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
Don't just watch, practice makes perfect
Practice topics for Differentiation
2.1
Definition of derivative
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