Çözüldü Üstel, Logaritmalı ve Trigonometrik Fonksiyon Türevi

https://i72.servimg.com/u/f72/19/97/10/39/zstel_10.png
https://scontent.fayt2-1.fna.fbcdn....=6b41821bf5c16e709ed1693c00554020&oe=5F2260A2
https://www.facebook.com/photo.php?fbid=3066029803492482&set=gm.1954214514716082&type=3&theater

z = e^[ g(x) ] ⇒ ln(z) = [ g(x) ]·ln(e) = [ g(x) ]·1 = g(x)
z ' / z = g '(x) ⇒ z ' = z·[ g '(x) ] = { e^[ g(x) ] }·[ g '(x) ]

y = f(x) = x·[ e^(sinx + 1) ] - (sinx)·[ e^(x + 1) ]
y' = dy / dx = f '(x) = 1·[ e^(sinx + 1) ] + x·[ e^(sinx + 1) ]·(cosx + 0) - (cosx)·[ e^(x + 1) ] - (sinx)·[ e^(x + 1) ]·(1 + 0)
f '(0) = 1·[ e^(0 + 1) ] + 0·[ e^(0 + 1) ]·(1 + 0) - 1·[ e^(0 + 1) ] - 0·[ e^(0 + 1) ]·(1 + 0)
f '(0) = e + 0 - e - 0
f '(0) = 0
WolframAlpha Kontrolu:
https://www.wolframalpha.com/input/?i=f(x)=x*(e^(sin(x)+1))-(sin(x))*(e^(x+1)),f'(0)=?