What is the derivative of this function $x^(2)sin(1/x)$ ?

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Answer 1 · 2016-08-09T20:33:14

$2xsin(1/x)-cos(1/x)$

Use the product rule: $d/dx(uv)=u'v+uv'$ to get

$d/dx(x^2sin(1/x)) = [2x][sin(1/x)]+[x^2][cos(1/x)*(-1/x^2)]$

$= 2xsin(1/x)-cos(1/x)$

For all reals except $0$ .

What is the derivative of this function x^(2)sin(1/x) x^(2)sin(1/x)?