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Calculus

How To Debunk Fake Math Proofs?

Published on May 12, 2024 by Hemanth

How To Debunk Fake Math Proofs? - a = b; a*a = a*b; a*a - b*b = a*b - b*b; (a+b)*(a-b) = b*(a-b); a+b = b; 2b = b; 2 = 1
You spot one, you spot them all!
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Calculus XIII: How To Really Understand The Chain Rule

Published on December 2, 2022 by Hemanth

Calculus XIII: How To Really Understand The Chain Rule - Whiteboard style graphic illustration showing the following information: y = f(x) = (x² + 5)^(3/2); dy/dx = What (??)
In this 13th calculus series essay, we cover the chain rule of calculus. Learn the mathematical framework behind one of the most useful rules of calculus!
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Calculus XII: How To Deal With The Time Derivative

Published on November 18, 2022 by Hemanth

Calculus XII: How To Deal With The Time Derivative - An illustration of a car travelling at a fast rate on the left. The driver seems to be a smiling stick figure with a smug look. On the right, the following pink text is written inside a black box: "dx/dt = what ??"
In this 11th calculus series essay, we cover the time derivative. Learn the fundamental math behind the study of quantities that change with time!
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Calculus XI: How To Deal With Successive Differentiation?

Published on October 28, 2022 by Hemanth

Calculus XI: How To Deal With Successive Differentiation? - Whiteboard graphics showing the following illustration: dy/dx = Derivative; → d⁹/dx⁹ = ??
In this 11th calculus series essay, we cover successive differentiation. Learn the fundamentals behind higher order derivatives that are often used in science!
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Calculus (X): How To Really Understand The Quotient Rule

Published on October 17, 2022 by Hemanth

Calculus (X): How To Really Understand The Quotient Rule - Whiteboard graphics showing the following: u(x) = 6x² + a; v(x) = 2x + b; y(x) = (6x³ + a)/(2x + b) = u/v; 'a' and 'b' are constants; dy/dx = ??
In this 10th calculus series essay, we cover the quotient rule of differentiation. Learn how to actually use the first principles behind the quotient rule!
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Calculus (IX): How To Really Understand The Product Rule

Published on October 10, 2022 by Hemanth

Calculus (IX): How To Really Understand The Product Rule - An illustration with whiteboard graphics showing the following information: u(x) = 3x² + 2; v(x) = 2x + 8; y(x) = [u(x)]*[v(x)]; dy/dx = ??
In this 9th calculus series essay, we cover the product rule of differentiation. Learn how to actually use the first principles behind the product rule!
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Calculus (VIII): How To Learn The Sum Rule And The Difference Rule

Published on October 4, 2022 by Hemanth

Calculus (VIII): How To Learn Sum Rule And Difference Rule - An illustration showing the following information using white board graphics: u = f(x); v = f(x); y = f(x) = (u + v); → dy/dx = ??
In this 8th calculus essay, you learn the basic math behind the sum rule and the difference rule. Get to know WHY the rules of differentiation actually work!
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Calculus (VII): How To Differentiate Constants?

Published on September 26, 2022 by Hemanth

Calculus (VII): How To Differentiate Constants? - An illustration showing that d(ax²)/dx = 2ax. Below this equation, the following question is asked: "But How??"
The seventh entry in the calculus series — an account on how to differentiate constants. This essay uses the product rule to formally differentiate constants.
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Calculus (VI): How To Really Learn The Power Rule?

Published on September 18, 2022 by Hemanth

Calculus (VI): How To Really Learn The Power Rule? - An illustration showing that d(x²)/dx = 2x. Below this equation, the following question is asked: "But How??"
The power rule is arguably the most frequently used calculus rule. This essay presents the mathematical fundamentals behind this useful rule in detail!
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Calculus (V): How To Differentiate, Actually?

Published on September 14, 2022 by Hemanth

Calculus (V): How To Differentiate, Actually? - y = f(x) = x² → dy/dx = ??
Knowing how to differentiate is one of the fundamental prerequisites of calculus. Learn the math and motivation behind the ‘dy/dx’ computation in this essay!
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