Πίνακας Βασικών Παραγωγίσεων
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Πίνακας Βασικών Παραγωγίσεων
Transcript of Πίνακας Βασικών Παραγωγίσεων
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(f(x)g(x)) '=f ' (x)g'(x)
(c f(x))' = c f '(x) (f(x) g(x))' = f ' (x) g(x) + f(x) g' (x)
[ ]21 g (x)
g(x) g(x)
= [ ]2f (x) f (x)g(x) f (x)g (x)g(x) g(x)
=
(g o f)'(x) = g'(f(x)) f '(x)
(c)' = 0
(x)' = 1
( x ) ' = x - 1 , vN* ([f(x)]v)'=v [f(x)]v-1.f '(x)
( ) 1x2 x
= ( x > 0) ( ) 1f (x) f (x)2 f (x)
= f(x)>0
(x)' = x (f(x))' = f(x)f '(x)
(x)' = - x (f(x))' = - f(x) f '(x)
(lnx)' = 1x
, x > 0 (lnf(x))' = 1f (x)
f '(x), f(x) > 0
(ln|x|)'= 1x
( ln |f(x)| )' = 1f (x)
f '(x)
(x)' = 21
x ( ) 21f (x) f (x)f (x)
=
(x)' = 21
x ( ) 2
1f (x) f (x)f (x)
=
(ex)' = ex ( )f (x ) f (x)e e f (x) = (x)' =x ln ( )f (x) f (x) ln f (x) = ( x t )' = x t - 1 , tR, x > 0 [ ]( ) [ ]t t 1f (x) t f (x) f (x) =
