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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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17.
Derivatives
17.1
Definition of derivative
17.2
Power rule
17.3
Gradient and equation of tangent line
17.4
Chain rule
17.5
Derivative of trigonometric functions
17.6
Derivative of exponential functions
17.7
Product rule
17.8
Quotient rule
17.9
Implicit differentiation
17.10
Derivative of inverse trigonometric functions
17.11
Derivative of logarithmic functions
17.12
Higher order derivatives
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Practice topics for Derivatives
17.1
Definition of derivative
17.2
Power rule
17.3
Gradient and equation of tangent line
17.4
Chain rule
17.5
Derivative of trigonometric functions
17.6
Derivative of exponential functions
17.7
Product rule
17.8
Quotient rule
17.9
Implicit differentiation
17.10
Derivative of inverse trigonometric functions
17.11
Derivative of logarithmic functions
17.12
Higher order derivatives