Differentiate using the product rule

Question

Differentiate using the product rule d/dx [(cos x) * x]

Answer 1

Solving this requires utilizing the product rule:

d/dx [f(x)*g(x)] = d/dx[f(x)]*g(x) + f(x)*d/dx[g(x)]

Derivative of a product f(x)*g(x) Derivative of f(x) * g(x) f(x) * Derivative of g(x)

Applied in this case, the product rule produces:

d/dx [cos(x)*(x)] = d/dx[cos(x)]*(x) +cos(x)*d/dx[(x)]

= -(sin(x))*(x) + cos(x)*(1)

= -xsin(x) + cos(x)

d/dx [cos(x)*(x)] = -x*sin(x) + cos(x) (Answer)