# How do you differentiate f(x)=sin^2(1/x)^2 using the chain rule?

Jun 10, 2018

$- \frac{4 \sin \left(\frac{1}{x} ^ 2\right) \cos \left(\frac{1}{x} ^ 2\right)}{x} ^ 3$

#### Explanation:

Writing your function in the form

${\left(\sin \left(\frac{1}{x} ^ 2\right)\right)}^{2}$
and we get by the power and the chain rule

$2 \sin \left(\frac{1}{x} ^ 2\right) \cos \left(\frac{1}{x} ^ 2\right) \cdot 2 \left(\frac{1}{x}\right) \cdot \left(- \frac{1}{x} ^ 2\right)$
this is

$- \frac{4 \sin \left(\frac{1}{x} ^ 2\right) \cdot \cos \left(\frac{1}{x} ^ 2\right)}{x} ^ 3$