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

Find the derivative of sin(2x)cos(2x)

Answer

$-4\sin\left(2x\right)\cos\left(x\right)\sin\left(x\right)+8\sin\left(x\right)^{4}-8\sin\left(x\right)^2+2$

Step-by-step explanation

Problem

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

Applying an identity of double-angle cosine

$\frac{d}{dx}\left(\left(1-2\sin\left(x\right)^2\right)\sin\left(2x\right)\right)$

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Answer

$-4\sin\left(2x\right)\cos\left(x\right)\sin\left(x\right)+8\sin\left(x\right)^{4}-8\sin\left(x\right)^2+2$
$\frac{d}{dx}\left(\sin\left(2x\right)\cdot \cos\left(2x\right)\right)$

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.8 seconds