Mathematics

Problem

Let

y=\dfrac{(3x^{2}-2x)(\sin x+1)}{x^{3}}

. (i) Find

\dfrac{dy}{dx}

, expressing your answer as a single fraction in simplest form. (ii) Hence determine the slope of the tangent to the curve

y=f(x)

x=\pi

. (iii) Verify that

\dfrac{dy}{dx}

is undefined at

x=0

and state the reason in one sentence.