Home/Differential Calculus/A.3 Inverse trigonometric/FormulaA.3 Inverse trigonometricFormulaIn A.3 Inverse trigonometricFormulaCopy LaTeXddx(arccscx)=−1∣x∣x2−1,∣x∣>1\frac{d}{dx}(\operatorname{arccsc}x)=-\frac{1}{|x|\sqrt{x^2-1}},\qquad |x|>1dxd(arccscx)=−∣x∣x2−11,∣x∣>1TagsA.3 Inverse trigonometricDifferential calculusDerivativeDerivative formulaTableVariablesxxxIndependent variablef′f'f′Derivative of fffdxdxdxDifferential of xxxConditions∣x∣>1|x|>1∣x∣>1Found an error? Contact us.Related formulasRelatedFormuladdx(arcsecx)=1∣x∣x2−1,∣x∣>1\frac{d}{dx}(\operatorname{arcsec}x)=\frac{1}{|x|\sqrt{x^2-1}},\qquad |x|>1dxd(arcsecx)=∣x∣x2−11,∣x∣>1Open formulaOpen in sectionRelatedFormuladdx(arccotx)=−11+x2,x∈R\frac{d}{dx}(\operatorname{arccot}x)=-\frac{1}{1+x^2},\qquad x\in\mathbb{R}dxd(arccotx)=−1+x21,x∈ROpen formulaOpen in sectionRelatedFormuladdx(arctanx)=11+x2,x∈R\frac{d}{dx}(\arctan x)=\frac{1}{1+x^2},\qquad x\in\mathbb{R}dxd(arctanx)=1+x21,x∈ROpen formulaOpen in sectionRelatedFormuladdx(arccosx)=−11−x2,∣x∣<1\frac{d}{dx}(\arccos x)=-\frac{1}{\sqrt{1-x^2}},\qquad |x|<1dxd(arccosx)=−1−x21,∣x∣<1Open formulaOpen in sectionRelatedFormuladdx(\arcsinx)=11−x2,∣x∣<1\frac{d}{dx}(\arcsinx)=\frac{1}{\sqrt{1-x^2}},\qquad |x|<1dxd(\arcsinx)=1−x21,∣x∣<1Open formulaOpen in section