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# Find the derivative of $\cos\left(x\right)\left(2x-\sin\left(2x\right)\right)$

## Step-by-step Solution

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Solving: $\frac{d}{dx}\left(\cos\left(x\right)\left(2x-\sin\left(2x\right)\right)\right)$

###  Videos

$\left(-2x+\sin\left(2x\right)\right)\sin\left(x\right)+\cos\left(x\right)\left(2-2\cos\left(2x\right)\right)$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\cos\left(x\right)\left(2x-\sin\left(2x\right)\right)\right)$

Specify the solving method

1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\cos\left(x\right)$ and $g=2x-\sin\left(2x\right)$

$\frac{d}{dx}\left(\cos\left(x\right)\right)\left(2x-\sin\left(2x\right)\right)+\cos\left(x\right)\frac{d}{dx}\left(2x-\sin\left(2x\right)\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(\cos\left(x\right)\right)\left(2x-\sin\left(2x\right)\right)+\cos\left(x\right)\frac{d}{dx}\left(2x-\sin\left(2x\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of cos(x)(2x-sin(2x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=2x-\sin\left(2x\right). 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). Simplify the product -(2x-\sin\left(2x\right)). The derivative of a sum of two or more functions is the sum of the derivatives of each function.

$\left(-2x+\sin\left(2x\right)\right)\sin\left(x\right)+\cos\left(x\right)\left(2-2\cos\left(2x\right)\right)$

##  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(cos(x)(2x-sin(2x))) using the product ruleFind d/dx(cos(x)(2x-sin(2x))) using the quotient ruleFind d/dx(cos(x)(2x-sin(2x))) using logarithmic differentiation

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x
y
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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

### Main topic:

Differential Calculus

~ 0.13 s

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