[aygun0]

S-1) (x²−1)/(x²+1) turevi

S-2) y=ln(2x)

S-3) y=e^tanx

[Serkan A.]

C-1)

u=x²−1 => u'=2x
v=x²+1 => v'=2x

Bölümün türevi kuralından

u'.v-v'.u

v²

=

2x.(x²+1)-2x.(x²−1)

(x²+1)²

=

2x.[(x²+1)-(x²−1)]

(x²+1)²

=

4x

x⁴+2x²+1

C-2)

u=2x u'=2

y=ln(u) => y'=

u'

u

=

2

ln(2x)

C-3) u=tanx => u'=sec²x

y=e^u => y'=u'.e^u => y'=sec²x.e^tanx