I have this problem:
if $$u=x^3y$$ then calculate $du/dt$ while $$x^5 + y =t$$ and $$x^2 + y^3 = t^2$$
I know that I should use the chain rule, and solved the problem to this point: $$\frac{du}{dt}=\frac{du}{dx}.\frac{dx}{dt} + \frac{du}{dy}.\frac{dy}{dt}$$
$$\frac{du}{dx} = 3x^2y$$ $$\frac{du}{dy} = x^3$$
Differentiation of the first expression with respect to $t$: $$5x^4\frac{dx}{dt} + \frac{dy}{dt} = 1$$
Differentiation of the second expression with respect to $t$: $$2x\frac{dx}{dt} + 3y^2\frac{dy}{dt} = 2t$$
But I don't know what should I do now, should I substitute something or what? I dont know what should I exactly do when we have an implicit Differentiation with two or three expressions. Would really appreciate your help.