I need to show that $\underset{\sim}{v}=e^{-0.1t}(\underset{\sim}{u}+\underset{\sim}{j})-\underset{\sim}{j}$ satisfies the equation $\underset{\sim}{a}=-0.1\underset{\sim}{v}-10\underset{\sim}{j}$ where $\underset{\sim}{u}$ is the initial velocity vector, $\underset{\sim}{j}$ is the horizontal unit vector, $\underset{\sim}{a}$ is the acceleration vector and $\underset{\sim}{v}$ is the velocity vector.
However when I derive $\underset{\sim}{v}=e^{-0.1t}(\underset{\sim}{u}+\underset{\sim}{j})-\underset{\sim}{j}$ with respect to $t$ I get:
$\underset{\sim}{a}=-0.1e^{-0.1t}(\underset{\sim}{u}+\underset{\sim}{j})$
$=-0.1(\underset{\sim}{v}+\underset{\sim}{j})$, which is not the equation given. Does this question have a typo or have I done something wrong?