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

## Step-by-step Solution

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###  Solution

$-12\left(\sin\left(3x\right)+\cos\left(4x\right)\right)$
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##  Step-by-step Solution 

Problem to solve:

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

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1

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

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

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

Learn how to solve 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)}.

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind d/dx(4cos(3x)-3sin(4x)) using the product ruleFind d/dx(4cos(3x)-3sin(4x)) using the quotient ruleFind d/dx(4cos(3x)-3sin(4x)) using logarithmic differentiation

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x
y
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◻/◻
/
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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

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