# Step-by-step Solution

## Find the derivative of $\sin\left(2x\right)$ using the definition

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$2\cos\left(2x\right)$

## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(sin\left(2x\right)\right)$

Choose the solving method

1

Find the derivative of $\sin\left(2x\right)$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\sin\left(2x\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit

$\lim_{h\to0}\left(\frac{\sin\left(2\left(x+h\right)\right)-\sin\left(2x\right)}{h}\right)$

Learn how to solve definition of derivative problems step by step online.

$\lim_{h\to0}\left(\frac{\sin\left(2\left(x+h\right)\right)-\sin\left(2x\right)}{h}\right)$

Learn how to solve definition of derivative problems step by step online. Find the derivative of sin(2x) using the definition. Find the derivative of \sin\left(2x\right) using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \sin\left(2x\right). Substituting f(x+h) and f(x) on the limit. Multiply the single term 2 by each term of the polynomial \left(x+h\right). Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals 2x, and angle \beta equals 2h. Factoring by \sin\left(2x\right).

$2\cos\left(2x\right)$
SnapXam A2

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\frac{d}{dx}\left(sin\left(2x\right)\right)$

### Main topic:

Definition of Derivative

~ 0.2 s