Try NerdPal! Our new app on iOS and Android

Find the derivative of $4\sin\left(x\right)\cos\left(x\right)$

Step-by-step Solution

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

Final Answer

$4\cos\left(2x\right)$
Got another answer? Verify it here

Step-by-step Solution

Problem to solve:

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

Specify 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 differential calculus problems step by step online.

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

Unlock the first 2 steps of this solution!

Learn how to solve differential calculus problems step by step online. Find the derivative of 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).

Final Answer

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

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

Tips on how to improve your answer:

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

Main topic:

Differential Calculus

Related Formulas:

4. See formulas

Time to solve it:

~ 0.04 s