Inverse trig derivatives

Derivative of arcsin x \frac{d}{dx}\,\arcsin x = \frac{1}{\sqrt{1 - x^2}} The derivative of arcsin x is 1/√(1 − x²). See the proof from sin y = x, the chain rule form for arcsin(u), a graph and worked examples. Derivative of arccos x \frac{d}{dx}\,\arccos x = -\frac{1}{\sqrt{1 - x^2}} The derivative of arccos x is −1/√(1 − x²). See the proof, why it is the negative of the arcsin derivative, chain rule examples and a graph. Derivative of arctan x \frac{d}{dx}\,\arctan x = \frac{1}{1 + x^2} The derivative of arctan x is 1/(1 + x²). See the proof from tan y = x, chain rule examples like arctan(2x) and arctan(x²), and a graph. Derivative of arcsec x \frac{d}{dx}\,\operatorname{arcsec} x = \frac{1}{\lvert x\rvert\sqrt{x^2 - 1}} The derivative of arcsec x is 1/(|x|√(x² − 1)). See where the absolute value comes from, a proof via arccos(1/x), and chain rule examples. Derivative of arccot x \frac{d}{dx}\,\operatorname{arccot} x = -\frac{1}{1 + x^2} The derivative of arccot x is −1/(1 + x²). See the proof from cot y = x, the link to arctan, chain rule examples and a graph.