Implicit Differentiation: Step-by-Step Method with Examples
How to find dy/dx when y isn’t isolated. A 4-step implicit differentiation method with circle, x³+y³=6xy and trig examples, plus tangent lines.
Category: Derivatives
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Chain Rule Explained: Formula, Steps and 8 Examples
The chain rule differentiates composite functions: d/dx f(g(x)) = f'(g(x))·g'(x). Clear steps, 8 worked examples and the most common mistakes.
Quotient Rule: Formula, Memory Trick and Worked Examples
The quotient rule: (u/v)’ = (u’v − uv’)/v². Learn the “low d-high minus high d-low” trick, worked examples and when to avoid the rule.
Product Rule: Formula, Proof and Step-by-Step Examples
The product rule: (fg)’ = f’g + fg’. See why it works, a proof, worked examples with trig, exponentials and logs, and the triple product rule.
Power Rule for Derivatives: Formula, Proof and 10 Examples
The power rule says d/dx xⁿ = n·xⁿ⁻¹. Learn when it applies, how to use it with roots, fractions and negative exponents, with 10 examples.
Derivative of cos²(x): −sin(2x) with Two Methods
The derivative of cos²(x) is −2sin(x)cos(x) = −sin(2x). Two methods, plus sin²(x), cos(x²) and cos²(3x) worked examples.
Derivative of x^x: Logarithmic Differentiation Explained
The derivative of x^x is x^x(ln x + 1). Step-by-step logarithmic differentiation, why the power rule fails, and more examples.
Derivative of e^(2x): 2e^(2x) Step by Step
The derivative of e^(2x) is 2e^(2x). Learn why with the chain rule, plus e^(kx), e^(x²), e^(−x) and x·e^(2x) examples.
Derivative of √x: 1/(2√x) with Proof and Examples
The derivative of √x is 1/(2√x). See the power rule method, the limit proof, chain rule examples like √(x²+1), and common errors.
Derivative of arcsin(x) = 1/√(1−x²): Proof and Examples
The derivative of arcsin(x) is 1/√(1−x²) for −1 < x < 1. Proof, chain rule examples, and the arccos version with its minus sign.