Derivative

Types

• Total Derivative
• Complete Partial
• Explicit Partial
• Inexact Differential
• Material Derivative
• Convective Derivative
• Covariant Derivative

Derivative List

• $(f\pm g{)}^{\prime }(x)=f^{\prime }(x)\pm g^{\prime }(x)$
• $(f\cdot g{)}^{\prime }=f^{\prime }g+f{g}^{\prime }$
• $(\frac{f}{g}{)}^{\prime }=\frac{f^{\prime }g-f{g}^{\prime }}{g^2}$
• $\frac{d}{dx}(f(g(x))=f^{\prime }(g(x))\cdot g^{\prime }(x)$
• $(x^n{)}^{\prime }=n{x}^{n-1}$
• $(e^x{)}^{\prime }=e^x$
• $(\ln x{)}^{\prime }=\frac{1}{x}$
• $(\sin x{)}^{\prime }=\cos x$
• $(\cos x{)}^{\prime }=-\sin x$
• $(\tan x{)}^{\prime }={\sec }^{2}x$
• $(\csc x{)}^{\prime }=-\csc x\cot x$
• $(\sec x{)}^{\prime }=\sec x\tan x$
• $(\cot x{)}^{\prime }=-{\csc }^{2}x$
• $({\sin }^{-1}x{)}^{\prime }=\frac{1}{\sqrt{1-x^2}}$
• $({\cos }^{-1}x{)}^{\prime }=-\frac{1}{\sqrt{1-x^2}}$
• $({\tan }^{-1}x{)}^{\prime }=\frac{1}{1+x^2}$
• $({\csc }^{-1}x{)}^{\prime }=-\frac{1}{|x|\sqrt{x^2-1}}$
• ${\sec }^{-1}x{)}^{\prime }=\frac{1}{|x|\sqrt{x^2-1}}$
• $({\cot }^{-1}x{)}^{\prime }=-\frac{1}{1+x^2}$
• $({\sinh }^{-1}x{)}^{\prime }=\frac{1}{\sqrt{x^2+1}},x>1$
• $({\cosh }^{-1}x{)}^{\prime }=\frac{1}{\sqrt{x^2-1}},|x|<1$
• $({\tanh }^{-1}x)=\frac{1}{1-x^2},|x|<1$
• $({\text{csch}}^{-1}x{)}^{\prime }=-\frac{1}{|x|\sqrt{1+x^2}},x\ne 0$
• $({\text{sech}}^{-1}x{)}^{\prime }=-\frac{1}{x\sqrt{1-x^2}},0<x<1$
• $({\coth }^{-1}x{)}^{\prime }=\frac{1}{1-x^2},|x|>1$