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

Aug 9, 2016

$2 x \sin \left(\frac{1}{x}\right) - \cos \left(\frac{1}{x}\right)$

#### Explanation:

Use the product rule: $\frac{d}{\mathrm{dx}} \left(u v\right) = u ' v + u v '$ to get

$\frac{d}{\mathrm{dx}} \left({x}^{2} \sin \left(\frac{1}{x}\right)\right) = \left[2 x\right] \left[\sin \left(\frac{1}{x}\right)\right] + \left[{x}^{2}\right] \left[\cos \left(\frac{1}{x}\right) \cdot \left(- \frac{1}{x} ^ 2\right)\right]$

$= 2 x \sin \left(\frac{1}{x}\right) - \cos \left(\frac{1}{x}\right)$

For all reals except $0$.