Таблица производных
a’=0, a – число \[ (x^n)’=nx^{n-1} \] \[ (\sqrtх)’=\frac1 {2\sqrtх} ) \] \[ (\frac1x)’=-\frac{1}{x^2} \] (ex)’=ex \[ (a^x)’=a^xlna \] (sinx)’=cosx (cosx)’=-sinx \[ (lnx)’=\frac{1}{x} \] \[ (log_{a}x)’=\frac1{xlna} \] \[ ((tgx)’=\frac{1}{cos^2x} ) \] \[ (ctgx)’=-\frac1{sin^2x} \] \[ (arcsinx)’=\frac1{\sqrt{1-x^2}} \] \[ ( (arccosx)’=\frac{-1}{\sqrt{1-x^2}} ) \] \[ (arctgx)’=\frac1{1+x^2} \] \[ (arcctgx)’=\frac{ -1 }{ 1+x^2 } \]