Home/Differential Calculus/Exponentials and logarithms/Formula5.6. Exponentials and logarithmsFormulaIn 5.6. Exponentials and logarithmsFormulaCopy LaTeXddx[ln∣x∣]=1x,x≠0\frac{d}{dx}[\ln|x|]=\frac{1}{x},\qquad x\neq0dxd[ln∣x∣]=x1,x=0TagsDifferential calculusDerivativeDerivative formulaRuleExponentials and logarithmsVariablesxxxIndependent variablef′f'f′Derivative of fffdxdxdxDifferential of xxxln\lnlnNatural logarithmConditionsx≠0x\neq0x=0Found an error? Contact us.Related formulasRelatedFormuladdx[lnx]=1x,x>0\frac{d}{dx}[\ln x]=\frac{1}{x},\qquad x>0dxd[lnx]=x1,x>0Open formulaOpen in sectionRelatedFormuladdx[logax]=1xlna,a>0, a≠1, x>0\frac{d}{dx}[\log_a x]=\frac{1}{x\ln a},\qquad a>0,\ a\neq1,\ x>0dxd[logax]=xlna1,a>0, a=1, x>0Open formulaOpen in sectionRelatedFormuladdx[ax]=axlna,a>0\frac{d}{dx}[a^x]=a^x\ln a,\qquad a>0dxd[ax]=axlna,a>0Open formulaOpen in sectionRelatedFormuladdx[ex]=ex\frac{d}{dx}[e^x]=e^xdxd[ex]=exOpen formulaOpen in section