Answer: It's always so hard to determine the culprit in a situation like this. Generally, if the new growth is dying baack, that indicates a root problem. I wonder if the plant has stayed too wet. Jade plants generally like to dry out between waterings, so too much water could stress it. On the other hand, if it's only been outside a week, I'd be surprised if it had a chance to develop root rot. One other possibility: did you slowly acclimate the plant, or set it out and leave it? It could have gotten "sunburned". Indoor plants moved outdoors need to be acclimated, or hardened off, by gradually exposing them to outdoor conditions, especially strong sunlight and cool weather. Even though jade plants like sun, when grown indoors the leaves are relatively tender, and they need to be allowed to toughen up grandually to withstand the harsh sun.
I would prune off damaged growth and make sure the plant isn't staying too wet. Jade plants are usually pretty durable, so it might come back OK. If it looked fine up until last week before you put it out, then don't fertilize it now. It's generally best to fertilize actively growing plants, and yours sounds like it's struggling.
Inspect the plant for any sign of insect (or rodent) attack. Make sure the stems haven't been nibbled or otherwise damaged. I hope it recovers!
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