Find $\frac{dz}{dt}$ -
$z(x,y) = x^2y^3$ , $x(t)= 2t^3$ $y(t)= 3t^2$
First , this is the chain rule formula I am using -
$\frac{dz}{dt} = \frac{\partial z}{\partial x} . \frac{dx}{dt} + \frac{\partial z}{\partial y} . \frac{dy}{dt} $
I found that $ \frac{\partial z}{\partial x} = 2xy^3$ and $ \frac{\partial z}{\partial y} = 3x^2y^2$
I found that $\frac{dx}{dt} = 6t^2$ and $\frac{dy}{dt} = 6t$
Now when I substitute back into the formula, I don’t get the required answer of $1296t^{11}$ . Where did the $x$ and $y$ go ? Where did I go wrong ?