What would be the partial derivative of $\frac{\partial x}{\partial t}$ with respect to itself $\frac{\partial \dot x}{\partial x}$ be?

Question

For context, I'm trying to linearize the function $$\dot x^2 \sin x$$ about $a = 0$ using Taylor Series. I can't come up with how to solve the second term, $$\left.\frac{\partial f}{\partial x}\right|_{x=a}\ \times (x-a)$$ which is $$\left.\frac{\partial \dot x^2 \sin x}{\partial x}\right|_{x=a} \times (x-a)$$

Any help appreciated.