Tan x'in türevi 1+tan² x'tir.
Tan x'in Türevi Nedir ? Tan x'in türevi 1+tan² x'tir.
( t an x ) ′ = 1 + t a n 2 x
d x d ( t an x ) = 1 + t a n 2 x
Tan x'in Türevinin İspatı 1. Yol f ′ ( x ) = h → 0 lim h f ( x + h ) − f ( x ) ( t an x ) ′ = h → 0 lim h t an ( x + h ) − t an x
t an ( p + q ) = 1 − t an p . t an q t an p + t an q
( t an x ) ′ = h → 0 lim h 1 − t an x . t an h t an x + t an h − t an x
( t an x ) ′ = h → 0 lim h 1 − t an x . t an h t an x + t an h − t an x . ( 1 − t an x . t an h )
( t an x ) ′ = h → 0 lim h 1 − t an x . t an h t an x + t an h − t an x + t a n 2 x . t an h
( t an x ) ′ = h → 0 lim h 1 − t an x . t an h t an h + t a n 2 x . t an h
( t an x ) ′ = h → 0 lim h 1 − t an x . t an h t an h . ( 1 + t a n 2 x )
( t an x ) ′ = h → 0 lim [ h 1 . 1 − t an x . t an h t an h . ( 1 + t a n 2 x ) ]
( t an x ) ′ = h → 0 lim h . ( 1 − t an x . t an h ) t an h . ( 1 + t a n 2 x )
( t an x ) ′ = h → 0 lim ( h t an h . 1 − t an x . t an h 1 + t a n 2 x )
( t an x ) ′ = h → 0 lim h t an h . h → 0 lim 1 − t an x . t an h 1 + t a n 2 x
t → 0 l i m t t an t = 1
( t an x ) ′ = 1. 1 − t an x . t an 0 1 + t a n 2 x
( t an x ) ′ = 1 − t an x . t an 0 1 + t a n 2 x
t an 0 = 0
( t an x ) ′ = 1 − t an x .0 1 + t a n 2 x
( t an x ) ′ = 1 − 0 1 + t a n 2 x
( t an x ) ′ = 1 1 + t a n 2 x
( t an x ) ′ = 1 + t a n 2 x
2. Yol f ′ ( x ) = h → 0 lim h f ( x + h ) − f ( x ) ( t an x ) ′ = h → 0 lim h t an ( x + h ) − t an x
t an x = cos x s in x
( t an x ) ′ = h → 0 lim h cos ( x + h ) s in ( x + h ) − cos x s in x
( t an x ) ′ = h → 0 lim h cos x . cos ( x + h ) s in ( x + h ) . cos x − cos ( x + h ) . s in x
s in p . cos q − cos p . s in q = s in ( p − q )
( t an x ) ′ = h → 0 lim h cos x . cos ( x + h ) s in ( x + h − x )
( t an x ) ′ = h → 0 lim h cos x . cos ( x + h ) s in h
( t an x ) ′ = h → 0 lim [ h 1 . cos x . cos ( x + h ) s in h ]
( t an x ) ′ = h → 0 lim h . cos x . cos ( x + h ) s in h
( t an x ) ′ = h → 0 lim [ h s in h . cos x . cos ( x + h ) 1 ]
( t an x ) ′ = h → 0 lim h s in h . h → 0 lim cos x . cos ( x + h ) 1
t → 0 l i m t s in t = 1
( t an x ) ′ = 1. cos x . cos ( x + 0 ) 1
( t an x ) ′ = cos x . cos ( x + 0 ) 1
( t an x ) ′ = cos x . cos x 1
( t an x ) ′ = co s 2 x 1
3. Yol t an x = cos x s in x
( t an x ) ′ = ( cos x s in x ) ′
( v u ) ′ = v 2 u ′ . v − v ′ . u
( t an x ) ′ = co s 2 x ( s in x ) ′ . cos x − ( cos x ) ′ . s in x
( s in x ) ′ = cos x ( cos x ) ′ = − s in x
( t an x ) ′ = co s 2 x cos x . cos x − ( − s in x ) . s in x
( t an x ) ′ = co s 2 x co s 2 x + s i n 2 x
co s 2 x + s i n 2 x = 1
( t an x ) ′ = co s 2 x 1
co s 2 x 1 = ( cos x 1 ) 2
( t an x ) ′ = ( cos x 1 ) 2
cos x 1 = sec x
( t an x ) ′ = se c 2 x
( t an x ) ′ = 1 + t a n 2 x = co s 2 x 1 = se c 2 x