Home/Differential Calculus/Basic rules/Formula5.1. Basic rulesFormulaIn 5.1. Basic rulesFormulaCopy LaTeXddx[f(x)±g(x)]=f′(x)±g′(x)\frac{d}{dx}[f(x)\pm g(x)]=f'(x)\pm g'(x)dxd[f(x)±g(x)]=f′(x)±g′(x)TagsDifferential calculusDerivativeDerivative formulaRuleBasic rulesVariablesxxxIndependent variablefffFunctiongggSecond function or inner compositionf′f'f′Derivative of fffdxdxdxDifferential of xxxFound an error? Contact us.Related formulasRelatedFormuladdx[cf(x)]=cf′(x)\frac{d}{dx}[cf(x)]=cf'(x)dxd[cf(x)]=cf′(x)Open formulaOpen in sectionRelatedFormula(fg)′=f′g+fg′(fg)'=f'g+fg'(fg)′=f′g+fg′Open formulaOpen in sectionRelatedFormuladdx[xn]=nxn−1,n∈R, x>0 if n∉Z\frac{d}{dx}[x^n]=nx^{n-1},\qquad n\in\mathbb{R},\ x>0\ \text{if }n\notin\mathbb{Z}dxd[xn]=nxn−1,n∈R, x>0 if n∈/ZOpen formulaOpen in sectionRelatedFormuladdx[c]=0\frac{d}{dx}[c]=0dxd[c]=0Open formulaOpen in section