Evaluate $f^{\prime }\left(x\right)$ at $x=\frac{\pi }{4}$ if $f\left(x\right)=\cos x$.

A wave travels along a string, and its position in millimeters is described by $h\left(t\right)=15(2\cos t+1)$, for $t\ge 0$, where $t$ represents time in seconds. Determine the velocity of the wave, $v\left(t\right)=h^{\prime }\left(t\right)$.

Consider the equation below. Using differentiation, state if it is true or false.

$\frac{d}{dx}(2\cot x{\csc }^{2}x-8\cot x-6x)=-6{\cot }^{4}x$