Home/Differential Calculus/Differentiation rules/Derivatives of inverse trigonometric functionsSection 5.7Derivatives of inverse trigonometric functionsFormulaCopy LaTeXddx(\arcsinx)=11−x2,∣x∣<1\frac{d}{dx}(\arcsinx)=\frac{1}{\sqrt{1-x^2}},\qquad |x|<1dxd(\arcsinx)=1−x21,∣x∣<1∣x∣<1|x|<1∣x∣<1View detail →FormulaCopy LaTeXddx(arccosx)=−11−x2,∣x∣<1\frac{d}{dx}(\arccos x)=-\frac{1}{\sqrt{1-x^2}},\qquad |x|<1dxd(arccosx)=−1−x21,∣x∣<1∣x∣<1|x|<1∣x∣<1View detail →FormulaCopy LaTeXddx(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∈Rx∈Rx\in\mathbb{R}x∈RView detail →FormulaCopy LaTeXddx(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∣>1∣x∣>1|x|>1∣x∣>1View detail →FormulaCopy 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∣>1∣x∣>1|x|>1∣x∣>1View detail →FormulaCopy LaTeXddx(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∈Rx∈Rx\in\mathbb{R}x∈RView detail →
FormulaCopy LaTeXddx(\arcsinx)=11−x2,∣x∣<1\frac{d}{dx}(\arcsinx)=\frac{1}{\sqrt{1-x^2}},\qquad |x|<1dxd(\arcsinx)=1−x21,∣x∣<1∣x∣<1|x|<1∣x∣<1View detail →
FormulaCopy LaTeXddx(arccosx)=−11−x2,∣x∣<1\frac{d}{dx}(\arccos x)=-\frac{1}{\sqrt{1-x^2}},\qquad |x|<1dxd(arccosx)=−1−x21,∣x∣<1∣x∣<1|x|<1∣x∣<1View detail →
FormulaCopy LaTeXddx(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∈Rx∈Rx\in\mathbb{R}x∈RView detail →
FormulaCopy LaTeXddx(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∣>1∣x∣>1|x|>1∣x∣>1View detail →
FormulaCopy 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∣>1∣x∣>1|x|>1∣x∣>1View detail →
FormulaCopy LaTeXddx(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∈Rx∈Rx\in\mathbb{R}x∈RView detail →