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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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41.
Differentiation
41.1
Power rule
41.2
Slope and equation of tangent line
41.3
Chain rule
41.4
Derivative of trigonometric functions
41.5
Derivative of exponential functions
41.6
Product rule
41.7
Quotient rule
41.8
Derivative of logarithmic functions
41.9
Higher order derivatives
41.10
Rectilinear Motion: Derivative
41.11
Critical number & maximum and minimum values
Don't just watch, practice makes perfect
Practice topics for Differentiation
41.1
Power rule
41.2
Slope and equation of tangent line
41.3
Chain rule
41.4
Derivative of trigonometric functions
41.5
Derivative of exponential functions
41.6
Product rule
41.7
Quotient rule
41.8
Derivative of logarithmic functions
41.9
Higher order derivatives
41.10
Rectilinear Motion: Derivative
41.11
Critical number & maximum and minimum values