# Step-by-step Solution

## Find the derivative $\frac{d}{dx}\left(4\cos\left(3x\right)-3\sin\left(4x\right)\right)$ using the sum rule

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### Videos

$-12\sin\left(3x\right)-12\cos\left(4x\right)$

## Step-by-step Solution

Problem to solve:

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

Choose the solving method

1

The derivative of a sum of two or more functions is the sum of the derivatives of each function

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

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

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

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(4cos(3x)-3sin(4x)) using the sum rule. The derivative of a sum of two or more 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)}.

$-12\sin\left(3x\right)-12\cos\left(4x\right)$
SnapXam A2

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a
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x
y
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.
(◻)
+
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◻/◻
/
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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

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

### Main topic:

Sum Rule of Differentiation

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