Let \(z=x^2+y^2\), where \(x=t\) and \(y=2t\). Find \(dz/dt\).

Let \(z=xy\), where \(x=t^2\) and \(y=t+1\). Find \(dz/dt\).

Let \(z=e^{xy}\), where \(x=s+t\) and \(y=s-t\). Find \(\partial z/\partial s\).

Let \(z=x^2y\), where \(x=r\cos\theta\) and \(y=r\sin\theta\). Find \(\partial z/\partial r\).

Let \(w=x+y+z\), where \(x=t\), \(y=t^2\), and \(z=t^3\). Find \(dw/dt\).

Let \(z=\ln(x+y)\), where \(x=u^2\) and \(y=v^2\). Find \(\partial z/\partial u\).

Let \(z=x^2-y^2\), where \(x=3t\) and \(y=4t\). Find \(dz/dt\) at \(t=1\).

Let \(z=f(x,y)\), where \(x=s^2+t\) and \(y=st\). Express \(\partial z/\partial t\) in terms of \(f_x\) and \(f_y\).

Let \(z=x^2+y^2\), where \(x=u+v\) and \(y=u-v\). Find \(\partial z/\partial v\).

A differentiable function \(z=f(x,y)\) has \(f_x(2,1)=5\) and \(f_y(2,1)=-3\). If \(x=t^2+1\) and \(y=t\), find \(dz/dt\) at \(t=1\).