Answer: Spider plants are pretty resilient and I've even had them come back from the roots even when the tops are dead. There's nothing you need to do - allow the soil to dry out between waterings and cut off the dead plant parts. It should revive on its own. Spider plants are quite sensitive to chloride and flouride in the water so you can try using bottled water for yours; for some reason they don't like to have perlite in the potting mix; it can make the leaf tips turn brown because of the fluoride in the perlite. If your plant sends out new growth and it, too, begins to turn brown, you might try repotting in a perlite free mix. Best wishes with your spider plant!
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