Derivative of x^x, x^x^x, and an Introduction to Tetration and Hyper-Exponentiation

An exploration into the derivative of x^x and x^x^x, and the concept of tetration and other hyper-exponentiations.

Investment Algebra: How to Determine the Original Investment Amount from the Current Interest

How to determine the original investment amount solely from the interest amount — using algebra.

Troubleshooting: Evaluating a Trigonometric Integral Algebraically

How a trigonometric integral is evaluated incorrectly — and how to fix it.

Modular Arithmetic: Some Advanced Tricks in Finding the Least Positive Residue

How to evaluate the least positive residue using brute force, Fermat’s Little Theorem and Chinese Remainder Theorem.

How to Solve a System of Linear Equations with an Additional Parameter?

How to solve a system of linear equations, when a coefficient of a variable is itself a variable.

How to Solve the Triangle with A=30°, b=40, and a=10?

How to find the angles and the side lengths of a general triangle — using the law of sines.