Question

Someone explain me, please
f(x) = x sin x
f'(x) = sin x + x cos x
for some c, \(2\pi n 2\pi n cos(2\pi n+\dfrac {1}{n} \) why?

Answer 1

@Supreme_Kurt

Answer 2

the derivative of x sin x is found using the product rule

(uv)' = uv' + vu' where u and v are functions of x

Answer 3

the derivative of x is 1 and derivative of sin x is cos x

Answer 4

@welshfella yes sir, :)

Answer 5

not complete but the range of any angle, c, would be between 2 pi and 0

Answer 6

I think he makes mistake. It should be
\(2\pi~n<c<2\pi~n+\dfrac{1}{2}\) since we just focus on the left hand side, hence, ignore the right hand side

Answer 7

\(2\pi n< c\\1<cosc\\2\pi~n<ccosc\\2\pi~n+ sin(2\pi n)<ccos c+sin c\\f'(c) > 2\pi n\)