Answer: The stuff you are seeing is called sooty mold. Certain pesky insects, including whiteflies, scale, or aphids secrete a substance known as honeydew which supports the growth of the black, sooty mold.
Control the insects with sprays of an appropriate insecticide such as insecticidal soap or a lightweight, horticultural oil. Direct sprays upward from beneath the plant making sure to wet the undersides of all leaves and branches. Repeat spraying will likely be necessary to get the pests under control.
When you control the pests, the sooty mold will cease to be a problem.
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