Arcsin x'in türevi 1/√1-x²'dir.
Arcsin x'in Türevi Nedir ? Arcsin x'in türevi 1/√1-x²'dir.
( a rcs in x ) ′ = 1 − x 2 1
d x d ( a rcs in x ) = 1 − x 2 1
Arcsin x'in Türevinin İspatı 1. Yol f ′ ( x ) = h → 0 lim h f ( x + h ) − f ( x )
( a rcs in x ) ′ = h → 0 lim h a rcs in ( x + h ) − a rcs in x a rcs in ( x + h ) = U , s in U = x + h a rcs in x = V , s in V = x s in U − s in V = x + h − x s in U − s in V = h h → 0 , s in U − s in V → 0 , s in U → s in V , U → V ( a rcs in x ) ′ = U → V lim s in U − s in V U − V s in p − s in q = 2. s in 2 p − q . cos 2 p + q ( a rcs in x ) ′ = U → V lim 2. s in 2 U − V . cos 2 U + V U − V ( a rcs in x ) ′ = U → V lim s in 2 U − V . cos 2 U + V 2 1 . ( U − V ) ( a rcs in x ) ′ = U → V lim s in 2 U − V . cos 2 U + V 2 U − V ( a rcs in x ) ′ = U → V lim ( s in 2 U − V 2 U − V . cos 2 U + V 1 ) ( a rcs in x ) ′ = U → V lim s in 2 U − V 2 U − V . U → V lim cos 2 U + V 1 U → V , 2 U − V → 0 ( a rcs in x ) ′ = 2 U − V → 0 lim s in 2 U − V 2 U − V . U → V lim cos 2 U + V 1 t → 0 l i m s in t t = 1
( a rcs in x ) ′ = 1. cos 2 V + V 1
( a rcs in x ) ′ = cos 2 V + V 1
( a rcs in x ) ′ = cos 2 2 V 1
( a rcs in x ) ′ = cos V 1
s in V = x
cos V = 1 − x 2
( a rcs in x ) ′ = 1 − x 2 1
2. Yol y = a rcs in x
s in y = x
( s in y ) ′ = ( x ) ′
( s in u ) ′ = u ′ . cos u
y ′ . cos y = 1
y ′ = cos y 1
s in y = x
cos y = 1 − x 2
y ′ = 1 − x 2 1
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