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Power rule
- Lesson: 1a6:04
- Lesson: 1b4:10
- Lesson: 1c6:30
- Lesson: 2a2:56
- Lesson: 2b2:22
- Lesson: 2c1:09
- Lesson: 34:41
- Lesson: 4a2:54
- Lesson: 4b2:21
- Lesson: 5a6:38
- Lesson: 5b2:18
- Lesson: 5c6:55
Power rule
When using the Definition of Derivative, finding the derivative of a long polynomial function with large exponents, or powers, can be very demanding. To avoid this, we introduce you one of the most powerful differentiation tools that simplifies this entire differentiation process – the Power Rule. In this section, we will see how the Power Rule allows us to easily derive the slope of a polynomial function at any given point.
Lessons
POWER RULE: dxd(xn)=nxn−1 , where n is any real number
- 1.power rule: dxd(xn)=nxn−1a)dxd(x5)b)dxd(x)c)dxd(3)
- 2.constant multiple rule: dxd[cf(x)]=cdxdf(x)a)dxd(4x3)b)dxd(6x)c)dxd(−x)
- 3.dxd(x10−5x7+31x4−20x3+x2−8x−1000)
sum rule: dxd[f(x)+g(x)]=dxdf(x)+dxdg(x)
difference rule: dxd[f(x)−g(x)]=dxdf(x)−dxdg(x)
- 4.negative exponents: x1=x−1 and xn1=x−na)dxd(x21)b)dxd(3x−5)
- 5.rational exponents: x=x21 and bxa=xbaa)dxd(3x5)b)dxd(x)c)dxd(21x38)
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2.
Derivatives
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 Derivatives
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