Cot 2x'in Türevi

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April 14, 2025

Cot 2x'in türevi -2.(1+cot² 2x)'tir.

cot 2x türevi.png

Cot 2x'in Türevi Nedir ?

Cot 2x'in türevi -2.(1+cot² 2x)'tir.

$(co t 2 x)^{'} = - 2. (1 + co t^{2} 2 x)$

$\frac{d}{d x} (co t 2 x) = - 2. (1 + co t^{2} 2 x)$

Cot 2x'in Türevinin İspatı

1. Yol

$f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{co t 2 ( x + h ) - co t 2 x}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{co t ( 2 x + 2 h ) - co t 2 x}{h}$

$co t (p + q) = \frac{co t p . co t q - 1}{co t p + co t q}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{co t 2 x . co t 2 h - 1}{co t 2 x + co t 2 h} - co t 2 x}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{co t 2 x . co t 2 h - 1 - co t 2 x . ( co t 2 x + co t 2 h )}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{co t 2 x . co t 2 h - 1 - co t ^{2} 2 x - co t 2 x . co t 2 h}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{- 1 - co t ^{2} 2 x}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{- ( 1 + co t ^{2} 2 x )}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim [\frac{1}{h} . \frac{- ( 1 + co t ^{2} 2 x )}{co t 2 x + co t 2 h}]$

$(co t 2 x)^{'} = h \to 0 lim \frac{- ( 1 + co t ^{2} 2 x )}{h . ( co t 2 x + co t 2 h )}$

$(co t 2 x)^{'} = h \to 0 lim \frac{- 2. ( 1 + co t ^{2} 2 x )}{2. h . ( co t 2 x + co t 2 h )}$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{1 + co t ^{2} 2 x}{2 h . ( co t 2 x + co t 2 h )}$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{1 + co t ^{2} 2 x}{2 h . co t 2 x + 2 h . co t 2 h}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{h \to 0 lim ( 2 h . co t 2 x + 2 h . co t 2 h )}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{h \to 0 lim ( 2 h . co t 2 x ) + h \to 0 lim ( 2 h . co t 2 h )}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{co t 2 x . h \to 0 lim 2 h + h \to 0 lim ( 2 h . co t 2 h )}$

$h \to 0 (2 h = h)$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{co t 2 x . h \to 0 lim h + h \to 0 lim ( h . co t h )}$

$t \to 0 l i m (t . co t t) = 1$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{co t 2 x .0 + 1}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{0 + 1}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{1}$

$(co t 2 x)^{'} = - 2. (1 + co t^{2} 2 x)$

2. Yol

$f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{co t 2 ( x + h ) - co t 2 x}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{co t ( 2 x + 2 h ) - co t 2 x}{h}$

$co t x = \frac{cos x}{s in x}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{cos ( 2 x + 2 h )}{s in ( 2 x + 2 h )} - \frac{cos 2 x}{s in 2 x}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{s in 2 x . cos ( 2 x + 2 h ) - cos 2 x . s in ( 2 x + 2 h )}{s in 2 x . s in ( 2 x + 2 h )}}{h}$

$s in p . cos q - cos p . s in q = s in (p - q)$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{s in [ 2 x - ( 2 x + 2 h )]}{s in 2 x . s in ( 2 x + 2 h )}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{s in ( 2 x - 2 x - 2 h )}{s in 2 x . s in ( 2 x + 2 h )}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{s in ( - 2 h )}{s in 2 x . s in ( 2 x + 2 h )}}{h}$

$s in (- x) = - s in x$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{- s in 2 h}{s in 2 x . s in ( 2 x + 2 h )}}{h}$

$(co t 2 x)^{'} = h \to 0 lim [\frac{1}{h} . \frac{- s in 2 h}{s in 2 x . s in ( 2 x + 2 h )}]$

$(co t 2 x)^{'} = h \to 0 lim \frac{- s in 2 h}{h . s in 2 x . s in ( 2 x + 2 h )}$

$(co t 2 x)^{'} = h \to 0 lim \frac{- 2. s in 2 h}{2. h . s in 2 x . s in ( 2 x + 2 h )}$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{s in 2 h}{2 h . s in 2 x . s in ( 2 x + 2 h )}$

$(co t 2 x)^{'} = - 2. h \to 0 lim [\frac{s in 2 h}{2 h} . \frac{1}{s in 2 x . s in ( 2 x + 2 h )}]$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{s in 2 h}{2 h} . h \to 0 lim \frac{1}{s in 2 x . s in ( 2 x + 2 h )}$

$h \to 0 (2 h = h)$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{s in h}{h} . h \to 0 lim \frac{1}{s in 2 x . s in ( 2 x + h )}$

$t \to 0 l i m \frac{s in t}{t} = 1$

$(co t 2 x)^{'} = - 2.1. \frac{1}{s in 2 x . s in ( 2 x + 0 )}$

$(co t 2 x)^{'} = - 2.1. \frac{1}{s in 2 x . s in 2 x}$

$(co t 2 x)^{'} = - \frac{2.1.1}{s i n ^{2} 2 x}$

$(co t 2 x)^{'} = - \frac{2}{s i n ^{2} 2 x}$

$(co t 2 x)^{'} = - 2. \frac{1}{s i n ^{2} 2 x}$

$(co t 2 x)^{'} = - 2. (\frac{1}{s in 2 x})^{2}$

$\frac{1}{s in x} = csc x$

$(co t 2 x)^{'} = - 2. cs c^{2} 2 x$

$(co t 2 x)^{'} = - 2. (1 + co t^{2} 2 x) = - \frac{2}{s i n ^{2} 2 x} = - 2. cs c^{2} 2 x$

# trigonometri # türev # kotanjant

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Cot 2x'in Türevi

Cot 2x'in Türevi Nedir ?

Cot 2x'in Türevinin İspatı

1. Yol

f′ (x)=h→0lim​hf (x+h)−f (x)​

(cot 2x)′=h→0lim​hcot 2(x+h)−cot 2x​

(cot 2x)′=h→0lim​hcot (2x+2h)−cot 2x​

cot (p+q)=cot p+cot qcot p.cot q−1​​

(cot 2x)′=h→0lim​hcot 2x+cot 2hcot 2x.cot 2h−1​−cot 2x​

(cot 2x)′=h→0lim​hcot 2x+cot 2hcot 2x.cot 2h−1−cot 2x.(cot 2x+cot 2h)​​

(cot 2x)′=h→0lim​hcot 2x+cot 2hcot 2x.cot 2h−1−cot2 2x−cot 2x.cot 2h​​

(cot 2x)′=h→0lim​hcot 2x+cot 2h−1−cot2 2x​​

(cot 2x)′=h→0lim​hcot 2x+cot 2h−(1+cot2 2x)​​

(cot 2x)′=h→0lim​ [h1​.cot 2x+cot 2h−(1+cot2 2x)​]

(cot 2x)′=h→0lim​2.h.(cot 2x+cot 2h)−2.(1+cot2 2x)​

(cot 2x)′=−2.h→0lim​2h.(cot 2x+cot 2h)1+cot2 2x​

(cot 2x)′=−2.h→0lim​2h.cot 2x+2h.cot 2h1+cot2 2x​

(cot 2x)′=−2.h→0lim​ (2h.cot 2x+2h.cot 2h)1+cot2 2x​

(cot 2x)′=−2.h→0lim​ (2h.cot 2x)+h→0lim​ (2h.cot 2h)1+cot2 2x​

(cot 2x)′=−2.cot 2x.h→0lim​2h+h→0lim​ (2h.cot 2h)1+cot2 2x​

t→0lim​ (t.cot t)=1​

(cot 2x)′=−2.cot 2x.0+11+cot2 2x​

2. Yol

f′ (x)=h→0lim​hf (x+h)−f (x)​

Share Your Expertise, Earn Rewards!

$f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{co t 2 ( x + h ) - co t 2 x}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{co t ( 2 x + 2 h ) - co t 2 x}{h}$

$co t (p + q) = \frac{co t p . co t q - 1}{co t p + co t q}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{co t 2 x . co t 2 h - 1}{co t 2 x + co t 2 h} - co t 2 x}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{co t 2 x . co t 2 h - 1 - co t 2 x . ( co t 2 x + co t 2 h )}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{co t 2 x . co t 2 h - 1 - co t ^{2} 2 x - co t 2 x . co t 2 h}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{- 1 - co t ^{2} 2 x}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim \frac{\frac{- ( 1 + co t ^{2} 2 x )}{co t 2 x + co t 2 h}}{h}$

$(co t 2 x)^{'} = h \to 0 lim [\frac{1}{h} . \frac{- ( 1 + co t ^{2} 2 x )}{co t 2 x + co t 2 h}]$

$(co t 2 x)^{'} = h \to 0 lim \frac{- 2. ( 1 + co t ^{2} 2 x )}{2. h . ( co t 2 x + co t 2 h )}$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{1 + co t ^{2} 2 x}{2 h . ( co t 2 x + co t 2 h )}$

$(co t 2 x)^{'} = - 2. h \to 0 lim \frac{1 + co t ^{2} 2 x}{2 h . co t 2 x + 2 h . co t 2 h}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{h \to 0 lim ( 2 h . co t 2 x + 2 h . co t 2 h )}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{h \to 0 lim ( 2 h . co t 2 x ) + h \to 0 lim ( 2 h . co t 2 h )}$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{co t 2 x . h \to 0 lim 2 h + h \to 0 lim ( 2 h . co t 2 h )}$

$t \to 0 l i m (t . co t t) = 1$

$(co t 2 x)^{'} = - 2. \frac{1 + co t ^{2} 2 x}{co t 2 x .0 + 1}$

$f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$