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**An equality for density+distribution funs of N(0,1)**

Reading through a book, I met the following equality (##F## is cumulative distribuion function, ##f## is density function)

$$\frac{d}{d\sigma}F_{N(0,\sigma^2)}(x)=\frac{-x}{\sigma}f_{N(0,\sigma^2)}(x)$$

which was given without any futher explanations (assumed obvious, I guess) but I have a hard time figuring out why it holds.

Could anyone, please, provide a hint on how to prove it?

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