65. If $x=\cos ^3 \theta-\sin ^3 \theta$ and $y=\sqrt[3]{\cos \theta}-\sqrt[3]{\sin \theta}$, then the value of $\frac{d y}{d x}$ at $\theta=\frac{\pi}{4}$ is

If $2 x^2+3 x y-y^2+4 x-5 y+6=0$, then the value of $\frac{d y}{d x}$ at $(x, y)=(1,-2)$ is

If $f(x)=|x-1|+|x-2|$, then

$$ f^{\prime}(-2023)+f^{\prime}\left(\frac{2024}{2023}\right)+f^{\prime}(2023)= $$

If $f(x)=\frac{e^{2 x}-e^{-2 x}}{e^{3 x}+e^{-3 x}}$, then $f^{\prime}(0)=$