Calculate the first, second, and third derivatives of the function $k\left(x\right)=2x^6+4x^5+9x^3$.

Find the second derivative of $f\left(x\right)=2\sin x-3\cos x$ with respect to $x$.

Given the differential equation $y^{\prime }$${}^{\prime }\left(t\right)+9y\left(t\right)=0$, which function below is a solution to this equation for all $t$?