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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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26.
Limits and Derivatives
26.1
Finding limits from graphs
26.2
Definition of derivative
26.3
Power rule
26.4
Slope and equation of tangent line
26.5
Chain rule
26.6
Derivative of trigonometric functions
26.7
Derivative of exponential functions
26.8
Product rule
26.9
Quotient rule
26.10
Implicit differentiation
26.11
Derivative of inverse trigonometric functions
26.12
Derivative of logarithmic functions
26.13
Higher order derivatives
Don't just watch, practice makes perfect
Practice topics for Limits and Derivatives
26.1
Finding limits from graphs
26.2
Definition of derivative
26.3
Power rule
26.4
Slope and equation of tangent line
26.5
Chain rule
26.6
Derivative of trigonometric functions
26.7
Derivative of exponential functions
26.8
Product rule
26.9
Quotient rule
26.10
Implicit differentiation
26.11
Derivative of inverse trigonometric functions
26.12
Derivative of logarithmic functions
26.13
Higher order derivatives