# Step-by-step Solution

## Find the derivative using the product rule $\frac{d}{dx}\left(4\sin\left(x\right)\cos\left(x\right)\right)$

Go!
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
|◻|
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

### Videos

$4\cos\left(2x\right)$

## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(4\sin\left(x\right)\cdot \cos\left(x\right)\right)$

Choose the solving method

1

The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function

$4\frac{d}{dx}\left(\sin\left(x\right)\cos\left(x\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$4\frac{d}{dx}\left(\sin\left(x\right)\cos\left(x\right)\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(4sin(x)*cos(x)). The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=\cos\left(x\right). 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)}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).

$4\cos\left(2x\right)$
SnapXam A2

### beta Got another answer? Verify it!

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
|◻|
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

$\frac{d}{dx}\left(4\sin\left(x\right)\cdot \cos\left(x\right)\right)$

### Main topic:

Product Rule of differentiation

~ 0.05 s