Home/Differential Calculus/Differentiation rules/Basic rulesSection 5.1Basic rulesFormulaCopy LaTeXddx[c]=0\frac{d}{dx}[c]=0dxd[c]=0View detail →FormulaCopy LaTeXddx[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∈/ZFor non-integer n∈Rn\in\mathbb{R}n∈R, valid on each interval where x>0x>0x>0 (or where xnx^nxn is defined and differentiable).n∈R, x>0 if n∉Zn\in\mathbb{R},\ x>0\ \text{if }n\notin\mathbb{Z}n∈R, x>0 if n∈/ZView detail →FormulaCopy LaTeXddx[cf(x)]=cf′(x)\frac{d}{dx}[cf(x)]=cf'(x)dxd[cf(x)]=cf′(x)View detail →FormulaCopy 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)View detail →
FormulaCopy LaTeXddx[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∈/ZFor non-integer n∈Rn\in\mathbb{R}n∈R, valid on each interval where x>0x>0x>0 (or where xnx^nxn is defined and differentiable).n∈R, x>0 if n∉Zn\in\mathbb{R},\ x>0\ \text{if }n\notin\mathbb{Z}n∈R, x>0 if n∈/ZView detail →
FormulaCopy 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)View detail →