Final Answer
Step-by-step Solution
Specify the solving method
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\cos\left(\frac{1}{x}\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(x\right)\cos\left(\frac{1}{x}\right)+x\frac{d}{dx}\left(\cos\left(\frac{1}{x}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of xcos(1/x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\cos\left(\frac{1}{x}\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). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.