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Master Exponential Function Derivatives: Techniques & Examples

Calculus 1: Master Core Concepts & Applications

Limits

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Intermediate value theorem

Proving the Existence of Real Roots Using IVT

Intermediate Value Theorem

Application of Intermediate Value Theorem

Proving the Existence of a Real Root Using IVT

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Finding limits from graphs  

Continuity

Discontinuities of Rational Functions (denominator=0)

Finding limits algebraically - direct substitution 

Finding limits algebraically - when direct substitution is not possible

Infinite limits - vertical asymptotes  

Limits at infinity - horizontal asymptotes

Limit Evaluation

Limits at Infinity of Exponential Functions

Squeeze theorem

Quadratic Function with Integer Vertex

Limit laws

Evaluating Limits of Functions

limit laws

Evaluating Limits with specific limits given

Introduction to Calculus - Limits 

Differentiation

Estimating derivatives from a table

Slope and equation of tangent line

Chain rule

Chain Rule

Differentiation of Trigonometric Function

Differentiate Radical Functions with Chain Rule

Differentiate: Trigonometric Functions

Chain rule: Differentiate Trigonometric Functions

Differentiation of Exponential Function

Differentiation of Exponential Functions

Differentiation: Chain Rule with Logarithmic Functions

Differentiation of Logarithmic Function

Product rule

Quotient rule

Differentiation using Quotient Rule

Differentiation using Chain Rule and Quotient Rule

Derivative of inverse trigonometric functions

Definition of derivative  

Definition of Derivative

Definition of derivative

Derivative using Definition

Vertical Tangent Line of a Function

Applications to definition of derivative

Power rule

Power Rule

Application of the Power Rule

Power rule application

Applying Power Rule

Power Rule with Negative Exponents

Power rule with rational exponents

Power rule and rational exponents

Derivative of trigonometric functions  

Derivative of Trigonometric Functions

Derivative of Composite Trig Functions

Derivative of exponential functions

Derivative of Exponential Functions

Differentiation of Composite Functions

Derivative of power and exponential functions

Derivative of logarithmic functions

Derivative of log with arbitrary base

Derivative of Natural Logarithm Functions

Derivative of Logarithmic Functions

Implicit differentiation

Higher order derivatives

Higher Order Derivatives

First and second derivatives

First and Second Derivatives

Second derivatives with implicit differentiation

Implicit Differentiation

Higher Order Derivatives with Repeating Patterns

Applications of differentiation

Mean value theorem 

Mean Value Theorem

Mean value theorem

Mean Value Theorem Application

Critical number & maximum and minimum values

Critical Number & Maximum and Minimum Values

Linear approximation

Use of Linear Approximations in Estimating Square Roots

Linearization of Radical Functions

Linearization of Polynomial Functions

Linearization of Rational Functions

Linearization of Exponential Functions

Linearization of Logarithmic Functions

Linear Approximation of Trigonometric Functions

Optimization

Position velocity acceleration

Velocity of a Particle

Total Distance Traveled by a Particle

Comparative Analysis of Particle's Velocity and Acceleration

Curve sketching

Related rates

l'Hospital's rule

l'Hopital's rule

l'Hospital's Rule

Evaluating the limit using L'Hospital's Rule

l"Hospital"s rule

Parent Assignments

Challenge Zone

Foundation Review

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Calculus 1

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Intro

Intro to differentiating exponential functions using the chain rule

Differentiating 3 to the power of 5 to the x squared using nested chain rule

Proving the derivative of e^x and applying the chain rule to e^(sin x)

Differentiating tan(cos(e^(5x²))) using repeated chain rule

Power rule vs exponential rule: avoiding a common mistake

An exponential function is a function containing a numerical <a href='[[glossary.html|{"keyword":"Base","term":"Base"}]]'>base</a> with at least one <a href="[[glossary.html|{"keyword":"Variable"}]]">variable</a> 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.

Finding the derivative of exponential functions

Mastering Derivatives of Exponential Functions

What You'll Learn

Apply the exponential differentiation formula c^x with natural logarithm of the base

Differentiate natural exponential functions e^x using the special property that d/dx(e^x) = e^x

Use the chain rule with bracket technique to differentiate composite exponential functions

Distinguish between power functions (x^n) and exponential functions (c^x) when differentiating

Combine exponential differentiation with trigonometric derivatives in nested functions

What You'll Practice

Differentiating exponential functions with constant bases like 2^x and 3^x

Applying chain rule to exponentials with variable exponents like e^(sin x) and 2^(4x³)

Solving multi-layer composite functions involving exponential, trigonometric, and power functions

Distinguishing when to use power rule versus exponential rule based on function structure

Why This Matters

This Unit Includes

5 Video lessons

Practice exercises

Learning resources

Skills

Exponential Functions

Chain Rule

Natural Logarithm

e^x Derivative

Composite Functions

Bracket Technique

Power vs Exponential