John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 30, 2023
Calculus

How to Find the Derivative of b^x | Exploring Logarithmic Differentiation

Derivative of b^x The derivative of b^x, where b is a constant, can be found using logarithmic differentiation The derivative of b^x, where b is a constant,...

John Rhodes
July 30, 2023
Calculus

Understanding the Derivative of Logarithm Function with Base b Using Logarithmic Differentiation

Derivative of log base b of x The derivative of the logarithm function with base b, denoted as log base b of x or logₐ(x), can be...

John Rhodes
July 30, 2023
Calculus

Understanding the notation ln | Simplifying the equation ln(x^r) using logarithmic rules

ln (x^r) = To solve this equation, let’s first understand what the notation ln represents To solve this equation, let’s first understand what the notation ln represents....

John Rhodes
July 30, 2023
Calculus

Calculating Average Rate of Change | Definition, Formula, and Example

Average Rate of Change The average rate of change refers to the average rate at which one quantity changes in relation to another over a specific interval...

John Rhodes
July 30, 2023
Calculus

Understanding Instantaneous Rate of Change | Calculating The Slope at a Specific Point of a Function

Instantaneous Rate of Change The instantaneous rate of change refers to the rate at which a function is changing at a specific point, or instant, on its...

John Rhodes
July 30, 2023
Calculus

Understanding the Relationship Between a Function’s Increasing Behavior and its First Derivative

If a function is increasing, its first derivative is ______________. If a function is increasing, its first derivative is positive If a function is increasing, its first...

John Rhodes
July 30, 2023
Calculus

The Relationship Between Decreasing Functions and Negative First Derivatives

If a function is decreasing, its first derivative is ______________. If a function is decreasing, its first derivative is negative If a function is decreasing, its first...

John Rhodes
July 30, 2023
Calculus

Understanding the Positive Second Derivative | Concave Up and Increasing Function

If f”(x) is > 0, then f”(x) is ___________ and f(x) is _____________. If f”(x) is greater than zero, it means that the second derivative of the...