Home/Differential Calculus/A.1 Powers and exponentials/FormulaA.1 Powers and exponentialsFormulaIn A.1 Powers and exponentialsFormulaCopy LaTeXddx[xn]=nxn−1,n∈R\frac{d}{dx}[x^n]=nx^{n-1},\qquad n\in\mathbb{R}dxd[xn]=nxn−1,n∈RTagsA.1 Powers and exponentialsDifferential calculusDerivativeDerivative formulaTableVariablesxxxIndependent variablef′f'f′Derivative of fffnnnDerivative order or exponentdxdxdxDifferential of xxxConditionsn∈Rn\in\mathbb{R}n∈RFound an error? Contact us.Related formulasRelatedFormuladdx[ex]=ex\frac{d}{dx}[e^x]=e^xdxd[ex]=exOpen 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[lnx]=1x,x>0\frac{d}{dx}[\ln x]=\frac{1}{x},\qquad x>0dxd[lnx]=x1,x>0Open formulaOpen in sectionRelatedFormuladdx[ln∣x∣]=1x,x≠0\frac{d}{dx}[\ln|x|]=\frac{1}{x},\qquad x\neq0dxd[ln∣x∣]=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 section