Mathc initiation/a0073
Calculons la dérivée :
cos(x+h) - cos(x)
cos(x)' = lim -----------------
h->0 h
(cos(x)cos(h)- sin(x)sin(h)) - cos(x)
cos(x)' = lim ------------------------------------
h->0 h
(cos(x)cos(h) - cos(x)) - sin(x)sin(h)
cos(x)' = lim --------------------------------------
h->0 h
cos(x) (cos(h)-1) sin(x)sin(h)
cos(x)' = lim ----------------- - lim ------------
h->0 h h->0 h
(cos(h)-1) sin(h)
cos(x)' = cos(x) lim ---------- - sin(x) lim ------
h->0 h h->0 h
cos(x)' = cos(x) 0 - sin(x) 1
cos(x)' = -sin(x)
Remarque :