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Compute derivatives of F(t) = cosh t i + sinh (2t) j + e-3tk

Compute the derivatives F'(t) and F''(t) of the vector valued function

    \[ F(t) = \cosh t \mathbf{i} + \sinh (2t) \mathbf{j} + e^{-3t} \mathbf{k}. \]


We compute

    \begin{align*}  F'(t) &= \sinh t \mathbf{i} + 2 \cosh (2t) \mathbf{j} - 3e^{-3t} \mathbf{k} \\  F''(t) &= \cosh t \mathbf{i} + 4 \sinh (2t) \mathbf{j} + 9e^{-3t} \mathbf{k}. \end{align*}

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