Here, we show you a step-by-step solved example of higher-order derivatives. This solution was automatically generated by our smart calculator:
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\cos\left(x\right)$
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 $f'(x) = -\sin(x)\cdot D_x(x)$
The derivative of the linear function is equal to $1$
Find the ($1$) derivative
The derivative of a sum of two or more functions is the sum of the derivatives of each function
The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\sin\left(x\right)$
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 ${f'(x) = \cos(x)\cdot D_x(x)}$
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 $f'(x) = -\sin(x)\cdot D_x(x)$
The derivative of the linear function is equal to $1$
Multiply the single term $-1$ by each term of the polynomial $\left(\sin\left(x\right)+x\cos\left(x\right)\right)$
Combining like terms $-\sin\left(x\right)$ and $-\sin\left(x\right)$
Find the ($2$) derivative
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