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Derivative of exponential functions
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- Lesson: 43:41
Derivative of exponential functions
An exponential function is a function containing a numerical base with at least one variable in its exponent. In this section, we will learn how to differentiate exponential functions, including natural exponential functions and other composite functions that require the application of the Chain Rule.
Lessons
Differential Rules – Exponential Functions
dxdcx=cx⋅lnc
dxdc()=c()⋅lnc⋅dxd()
dxdex=ex
dxde()=e()⋅dxd()
dxdcx=cx⋅lnc
dxdc()=c()⋅lnc⋅dxd()
dxdex=ex
dxde()=e()⋅dxd()
- Introductiondxd2x
dxd24x3 - 1.dxd35x2
- 2.dxdex
dxdesinx - 3.Differentiate:
y=tan(cose5x2) - 4.dxdx5 VS. dxd5x
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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
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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