# Step-by-step Solution

## Find the higher order derivative of $x\cos\left(x\right)$

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asin
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sinh
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asinh
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### Videos

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

## Step-by-step explanation

Problem to solve:

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

Rewriting the high order derivative

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

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

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

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

### Main topic:

Differential calculus

~ 0.57 seconds

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