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# Higher-order derivatives Calculator

## Get detailed solutions to your math problems with our Higher-order derivatives step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of higher-order derivatives. This solution was automatically generated by our smart calculator:

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

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=$\frac{d}{dx}\left(x\right)\cos\left(x\right)+x\frac{d}{dx}\left(\cos\left(x\right)\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)\frac{d}{dx}\left(x\right)\cos\left(x\right)-x\sin\left(x\right)$The derivative of the linear function is equal to$1\cos\left(x\right)-x\sin\left(x\right)$2 Find the ($1$) derivative$\cos\left(x\right)-x\sin\left(x\right)$The derivative of a sum of two or more functions is the sum of the derivatives of each function$\frac{d}{dx}\left(\cos\left(x\right)\right)+\frac{d}{dx}\left(-x\sin\left(x\right)\right)$The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function$\frac{d}{dx}\left(\cos\left(x\right)\right)-\frac{d}{dx}\left(x\sin\left(x\right)\right)$Apply the product rule for differentiation:$(f\cdot g)'=f'\cdot g+f\cdot g'$, where$f=

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

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 ${f'(x) = \cos(x)\cdot D_x(x)}$

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

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

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

The derivative of the linear function is equal to $1$

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

Multiply the single term $-1$ by each term of the polynomial $\left(\sin\left(x\right)+x\cos\left(x\right)\right)$

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

Combining like terms $-\sin\left(x\right)$ and $-\sin\left(x\right)$

$-2\sin\left(x\right)-x\cos\left(x\right)$
3

Find the ($2$) derivative

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

##  Final answer to the problem

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

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