The Chain Rule: How It Works, With Worked Examples
Learn the chain rule step by step: what it says, why it works, how to spot the inside function, and worked examples with powers, trig, e^x and ln.
· 5 min read
Derivatives
Derivative rules explained step by step, from the power rule to implicit differentiation.
Derivatives of Exponential and Log Functions: e^x, a^x and ln x
Learn the derivatives of e^x, a^x, ln x and log base a, why e is special, and how logarithmic differentiation handles x^x and messy products.
· 6 min read
Derivatives of Trig Functions: All Six, With Proofs and Examples
The derivatives of sin, cos, tan, cot, sec and csc, why the derivative of sin x is cos x, and worked chain rule examples with trig functions.
· 7 min read
Implicit Differentiation: Step-by-Step Method and Examples
Learn implicit differentiation step by step: find dy/dx for circles and curves you cannot solve for y, find tangent lines, and compute the second derivative.
· 6 min read
The Limit Definition of the Derivative, Step by Step
Learn the limit definition of the derivative: the difference quotient, secant lines becoming tangent lines, and worked examples for x², 1/x and √x.
· 7 min read
The Power Rule for Derivatives: Rules, Examples and Tricks
Master the power rule: how it works, negative and fractional exponents, rewriting roots and fractions, plus the sum and constant multiple rules.
· 7 min read
Product and Quotient Rules: Formulas, Mnemonics and Examples
Learn the product rule and quotient rule step by step, with easy mnemonics, when to simplify first, and fully worked derivative examples.
· 8 min read
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