IM14

Pochodne funkcji elementarnych:

x^a'= ax^a-^1sinx' = cosx	arctgx' - 1+>{2
cosx' = -sinx tgx' = —k- = 1 +tg^2x ^3 C0S^2X ^3	arcctgx' - 1+>{2 e*^1 = e^x
^ctgx' sin^2x --(^1+ct9^2x)	a*^1 = a^xlna ln|x|' = 1/x
• , 1 arcsinx - ,-	^|O0‘M' = SiFi =
-1 arccosx - ,— \TT>ć	\/x' = 1/(n x/x"^)

Twierdzenia o pochodnych:

[c*f(x)]'=c*f(x)

[f(x)-g(x)]'=f(x)-g'(x)

[f(x)+g(x)]'=f'(x)+g^,(x)

f[g(x)]-f'[g(x)*g^,(x)

[f(x)*g(x)]-f'(x)*g(x)+g'(x)*f(x)

_r^f(x) _r_ '(x)*g(x)-g'(x)*f(x)