Fundamental Properties of Differentiation

Michael Green

6 min read

Next Topic - Derivatives of Sine and Cosine Functions

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Study Guide Overview

This study guide covers derivatives of exponential and logarithmic functions. It includes differentiation of eˣ, eᵏˣ, aeᵏˣ, aˣ, aᵏˣ, ln x, a ln x, and ln kx. The guide provides worked examples, practice questions, and a glossary of key terms like the chain rule and constant multiple rule. Key takeaways emphasize correct application of these rules and properties of logarithms.

#Derivative of Exponential and Logarithmic Functions

#Table of Contents

Derivative of the Exponential Function
Derivative of a Number Raised to the Power of x
Derivative of the Natural Logarithmic Function
Practice Questions
Glossary
Summary and Key Takeaways

#Derivative of the Exponential Function

#Differentiating $e^x$

The function $f(x) = e^x$ is unique because its rate of change is equal to itself.

$f'(x) = e^x$

#Differentiating $e^{kx}$

For the function $g(x) = e^{kx}$ , its rate of change is proportional to itself.

$g'(x) = k e^{kx}$

This result is due to the chain rule.

#Differentiating $a e^{kx}$

For a function with a constant multiple of the exponential, the differentiation fo...

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Previous Topic - Derivative Rules Next Topic - Derivatives of Sine and Cosine Functions

Fundamental Properties of Differentiation

Michael Green

6 min read

Next Topic - Derivatives of Sine and Cosine Functions

Listen to this study note

Study Guide Overview

#Derivative of Exponential and Logarithmic Functions

#Table of Contents

Derivative of the Exponential Function
Derivative of a Number Raised to the Power of x
Derivative of the Natural Logarithmic Function
Practice Questions
Glossary
Summary and Key Takeaways

#Derivative of the Exponential Function

#Differentiating $e^x$

The function $f(x) = e^x$ is unique because its rate of change is equal to itself.

$f'(x) = e^x$

#Differentiating $e^{kx}$

For the function $g(x) = e^{kx}$ , its rate of change is proportional to itself.

$g'(x) = k e^{kx}$

This result is due to the chain rule.

#Differentiating $a e^{kx}$

For a function with a constant multiple of the exponential, the differentiation fo...

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Give us your feedback and let us know how we can improve

Previous Topic - Derivative Rules Next Topic - Derivatives of Sine and Cosine Functions

Fundamental Properties of Differentiation

Michael Green

#Derivative of Exponential and Logarithmic Functions

#Table of Contents

#Derivative of the Exponential Function

#Differentiating exe^xex

#Differentiating ekxe^{kx}ekx

#Differentiating aekxa e^{kx}aekx

How are we doing?

Fundamental Properties of Differentiation

Michael Green

#Derivative of Exponential and Logarithmic Functions

#Table of Contents

#Derivative of the Exponential Function

#Differentiating exe^xex

#Differentiating ekxe^{kx}ekx

#Differentiating aekxa e^{kx}aekx

How are we doing?

#Differentiating $e^x$

#Differentiating $e^{kx}$

#Differentiating $a e^{kx}$

#Differentiating $e^x$

#Differentiating $e^{kx}$

#Differentiating $a e^{kx}$