Let be the function defined by h(x)= cases x^ 3 ( 1 x ), & x 0, 0, & x=0

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let hh be the function defined by h(x)={x3sin⁡(1x),x≠0,0,x=0.h(x)=\begin{cases} x^{3}\sin\left(\dfrac{1}{x}\right), & x\neq 0,\\ 0, & x=0. \end{cases} Determine h′(0)h'(0), or state that the derivative does not exist.

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