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.
Author: Yasir Hafeez
Yasir Hafeez is the founder and editor of Calculus Calc. He writes and checks step-by-step calculus guides and builds the site's interactive calculators.
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Derivative of arctan(x) = 1/(1+x²): Proof and Examples
The derivative of arctan(x) is 1/(1+x²). Step-by-step proof with implicit differentiation, chain rule examples and the link to integrals.
Derivative of sec(x) = sec(x)tan(x): Proof and Examples
The derivative of sec(x) is sec(x)tan(x). See the proof from 1/cos(x), the chain rule form, second derivative and worked examples.
Derivative of tan(x) = sec²(x): Proof and Examples
The derivative of tan(x) is sec²(x). Learn the quotient rule proof, the chain rule version for tan(g(x)), and worked examples.
Derivative of ln(x): Formula, Proof and Examples
The derivative of ln(x) is 1/x. See two short proofs, the chain rule version for ln(g(x)), worked examples and common mistakes.
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