# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Final Answer

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

## Step-by-step explanation

Problem to solve:

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

Choose the solving method

1

The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$

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

The derivative of the linear function times a constant, is equal to the constant

$2\cos\left(2x\right)\frac{d}{dx}\left(x\right)$
3

The derivative of the linear function is equal to $1$

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

## Final Answer

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

### Main topic:

Differential calculus

### Time to solve it:

~ 0.02 s (SnapXam)