Derivative of $$$\frac{\cosh{\left(u \right)}}{3}$$$
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Find $$$\frac{d}{du} \left(\frac{\cosh{\left(u \right)}}{3}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ with $$$c = \frac{1}{3}$$$ and $$$f{\left(u \right)} = \cosh{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\frac{\cosh{\left(u \right)}}{3}\right)\right)} = {\color{red}\left(\frac{\frac{d}{du} \left(\cosh{\left(u \right)}\right)}{3}\right)}$$The derivative of the hyperbolic cosine is $$$\frac{d}{du} \left(\cosh{\left(u \right)}\right) = \sinh{\left(u \right)}$$$:
$$\frac{{\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}}{3} = \frac{{\color{red}\left(\sinh{\left(u \right)}\right)}}{3}$$Thus, $$$\frac{d}{du} \left(\frac{\cosh{\left(u \right)}}{3}\right) = \frac{\sinh{\left(u \right)}}{3}$$$.
Answer
$$$\frac{d}{du} \left(\frac{\cosh{\left(u \right)}}{3}\right) = \frac{\sinh{\left(u \right)}}{3}$$$A