Question

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

Answer 1

`(df(x))/dx= (-2cos(1/x^2))/x^3`

Explanation:

This is a simple chain rule problem. It is a little easier if we write the equation as:
`f(x) = sin(x^-2)`

This reminds us that `1/x^2` can be differentiated the same way as any polynomial, by dropping the exponent and and reducing it by one.

The application of the chain rule looks like:
`d/dx sin(x^-2) = cos(x^-2)(d/dx x^-2)`
`= cos(x^-2)(-2x^-3)`
`= (-2cos(1/x^2))/x^3`