Home/Differential Calculus/Definition of the derivative/Formula4.1. Definition of the derivativeFormulaIn 4.1. Definition of the derivativeFormulaCopy LaTeXf′(a)=limx→af(x)−f(a)x−af'(a)=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}f′(a)=x→alimx−af(x)−f(a)TagsDifferential calculusDerivativeDefinition of the derivativeDerivative formulaVariablesxxxIndependent variableaaaPoint or real constantfffFunctionf′f'f′Derivative of fffFound an error? Contact us.Related formulasRelatedMore generally, by the chain rule:ddx∫ag(x)f(t) dt=f(g(x))g′(x).\frac{d}{dx}\int_a^{g(x)}f(t)\,dt=f(g(x))g'(x).dxd∫ag(x)f(t)dt=f(g(x))g′(x).Open formulaOpen in sectionRelatedFormulaf′(x)=limh→0f(x+h)−f(x)hf'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}f′(x)=h→0limhf(x+h)−f(x)Open formulaOpen in sectionRelatedFormulay−f(a)=f′(a)(x−a)y-f(a)=f'(a)(x-a)y−f(a)=f′(a)(x−a)Open formulaOpen in section