# Step-by-step Solution

## Find the derivative of 2cos(2*x)

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### Videos

$-4\sin\left(2x\right)$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(2\cos\left(2x\right)\right)$
1

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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

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 $f'(x) = -\sin(x)\cdot D_x(x)$

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

$-4\sin\left(2x\right)$
$\frac{d}{dx}\left(2\cos\left(2x\right)\right)$

### Main topic:

Differential calculus

~ 0.22 seconds