Home/Differential Calculus/Differentiation rules/Exponentials and logarithmsSection 5.6Exponentials and logarithmsFormulaCopy LaTeXddx[ex]=ex\frac{d}{dx}[e^x]=e^xdxd[ex]=exView detail →FormulaCopy LaTeXddx[ax]=axlna,a>0\frac{d}{dx}[a^x]=a^x\ln a,\qquad a>0dxd[ax]=axlna,a>0a>0a>0a>0View detail →FormulaCopy LaTeXddx[lnx]=1x,x>0\frac{d}{dx}[\ln x]=\frac{1}{x},\qquad x>0dxd[lnx]=x1,x>0x>0x>0x>0View detail →FormulaCopy LaTeXddx[ln∣x∣]=1x,x≠0\frac{d}{dx}[\ln|x|]=\frac{1}{x},\qquad x\neq0dxd[ln∣x∣]=x1,x=0x≠0x\neq0x=0View detail →FormulaCopy LaTeXddx[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>0a>0, a≠1, x>0a>0,\ a\neq1,\ x>0a>0, a=1, x>0View detail →
FormulaCopy LaTeXddx[ax]=axlna,a>0\frac{d}{dx}[a^x]=a^x\ln a,\qquad a>0dxd[ax]=axlna,a>0a>0a>0a>0View detail →
FormulaCopy LaTeXddx[lnx]=1x,x>0\frac{d}{dx}[\ln x]=\frac{1}{x},\qquad x>0dxd[lnx]=x1,x>0x>0x>0x>0View detail →
FormulaCopy LaTeXddx[ln∣x∣]=1x,x≠0\frac{d}{dx}[\ln|x|]=\frac{1}{x},\qquad x\neq0dxd[ln∣x∣]=x1,x=0x≠0x\neq0x=0View detail →
FormulaCopy LaTeXddx[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>0a>0, a≠1, x>0a>0,\ a\neq1,\ x>0a>0, a=1, x>0View detail →