Home/Calculus II/Notation, domains and conventions/Derivatives to recognize when integratingSection 1.1Derivatives to recognize when integratingFormulaCopy LaTeXddxln∣g(x)∣=g′(x)g(x)\frac{d}{dx}\ln|g(x)|=\frac{g'(x)}{g(x)}dxdln∣g(x)∣=g(x)g′(x)View detail →FormulaCopy LaTeXddxeg(x)=eg(x)g′(x)\frac{d}{dx}e^{g(x)}=e^{g(x)}g'(x)dxdeg(x)=eg(x)g′(x)View detail →FormulaCopy LaTeXddxarcsin (xa)=1a2−x2,a>0\frac{d}{dx}\arcsin\!\left(\frac{x}{a}\right) =\frac{1}{\sqrt{a^2-x^2}},\qquad a>0dxdarcsin(ax)=a2−x21,a>0a>0a>0a>0View detail →FormulaCopy LaTeXddxarctan (xa)=aa2+x2,a>0\frac{d}{dx}\arctan\!\left(\frac{x}{a}\right) =\frac{a}{a^2+x^2},\qquad a>0dxdarctan(ax)=a2+x2a,a>0a>0a>0a>0View detail →
FormulaCopy LaTeXddxln∣g(x)∣=g′(x)g(x)\frac{d}{dx}\ln|g(x)|=\frac{g'(x)}{g(x)}dxdln∣g(x)∣=g(x)g′(x)View detail →
FormulaCopy LaTeXddxeg(x)=eg(x)g′(x)\frac{d}{dx}e^{g(x)}=e^{g(x)}g'(x)dxdeg(x)=eg(x)g′(x)View detail →
FormulaCopy LaTeXddxarcsin (xa)=1a2−x2,a>0\frac{d}{dx}\arcsin\!\left(\frac{x}{a}\right) =\frac{1}{\sqrt{a^2-x^2}},\qquad a>0dxdarcsin(ax)=a2−x21,a>0a>0a>0a>0View detail →
FormulaCopy LaTeXddxarctan (xa)=aa2+x2,a>0\frac{d}{dx}\arctan\!\left(\frac{x}{a}\right) =\frac{a}{a^2+x^2},\qquad a>0dxdarctan(ax)=a2+x2a,a>0a>0a>0a>0View detail →