# 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

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(4\cos\left(3x\right)-3\sin\left(4x\right)\right)$

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

$\frac{d}{dx}\left(4\cos\left(3x\right)\right)+\frac{d}{dx}\left(-3\sin\left(4x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(4cos(3*x)-3sin(4*x)) using the sum rule. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-3) is equal to the constant times the derivative of the function. 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)}.

$-12\sin\left(3x\right)-12\cos\left(4x\right)$
$\frac{d}{dx}\left(4\cos\left(3x\right)-3\sin\left(4x\right)\right)$

### Main topic:

Sum rule of differentiation

### Time to solve it:

~ 0.05 s (SnapXam)