I know the formula for changing systems however i keep getting the wrong result and i can understand why. Here is my calculation: $A=\hat{y}$ $A_{i}=\left(0,1,0\right)\ \ \ $ $\bar{A}_{j}=\frac{dq^{i}}{d\bar{q}^{j}}A_{i}ּ\ \ \ $ $\bar{A}_{j}=\frac{dq^{2}}{d\bar{q}^{j}}\ \ \ A_{2}=\frac{dq^{2}}{d\bar{q}^{j}}=\left(\frac{\partial y}{\partial\rho},\frac{\partial y}{\partial\varphi},\frac{\partial y}{\partial z}\right)=\sin\left(\varphi\right)\hat{\rho}+\cos\left(\varphi\right)\rho\hat{\rho}$
this solution is wrong, Where is my mistake?