What is the derivative of this function f(x) = sin (1/x^2)f(x)=sin(1x2)?

1 Answer
JMicheli
Jul 13, 2016

(df(x))/dx= (-2cos(1/x^2))/x^3df(x)dx=−2cos(1x2)x3

Explanation:

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

This reminds us that 1/x^21x2 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)ddxsin(x−2)=cos(x−2)(ddxx−2)
= cos(x^-2)(-2x^-3)=cos(x−2)(−2x−3)
= (-2cos(1/x^2))/x^3=−2cos(1x2)x3

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