Understanding the chain rule in calculus
I keep making mistakes with the chain rule. For example: If f(x) = sin(x^2), how do I find f'(x)? Can someone explain the chain rule step by step with multiple examples?...
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Understanding matrix multiplication
I don't understand why matrix multiplication isn't commutative. AB ≠ BA in most cases. Can someone explain with examples why this is the case and when it might be equal?...
How do I find the derivative of e^(x²)?
I'm learning calculus and struggling with the chain rule. When I have e raised to x squared, how do I find the derivative? Can someone walk me through the steps?...
How to solve systems of linear equations?
What are the different methods to solve systems of linear equations? When should I use substitution vs elimination vs matrices?...
What is the difference between permutation and combination?
I always mix up when to use permutation vs combination formulas. Can someone give me a simple rule to remember and some examples?...
Understanding logarithm properties
I'm confused about log rules. Can someone explain log(ab) = log(a) + log(b) and other properties with examples?...
Probability: Independent vs Mutually Exclusive events
What's the difference between independent events and mutually exclusive events? I keep confusing them in probability problems....
Eigenvalues and eigenvectors intuition
I can compute eigenvalues and eigenvectors but I don't understand what they mean geometrically. Can someone explain the intuition?...
Taylor series expansion explained
How do I expand a function as a Taylor series? What's the intuition behind it and when is it useful?...
How to prove something by mathematical induction?
I'm learning proof techniques and mathematical induction confuses me. How do I: 1. Identify the base case 2. State the inductive hypothesis 3. Prove the inductive step Can someone walk through provi...
Understanding the Fourier Transform
How does the Fourier Transform work? I understand it converts time domain to frequency domain but the math is confusing....
Proof that √2 is irrational
I'm trying to understand the classic proof by contradiction that √2 is irrational. Can someone explain each step clearly?...