** Final Answer

**

** Step-by-step Solution **

Problem to solve:

** Specify the solving method

**

**

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\cos\left(x^2-1\right)$

Learn how to solve differential calculus problems step by step online.

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

Learn how to solve differential calculus problems step by step online. Find the derivative of xcos(x^2-1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\cos\left(x^2-1\right). The derivative of the linear function is equal to 1. 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 a sum of two or more functions is the sum of the derivatives of each function.

** Final Answer

**