How can I express $\frac{dy}{dx}$ if I make the change of variable $x-1 = t$? If $y$ is a function of x and I make the change of variable $x-1=t$. Now what would $\frac{dy}{dx}$ equal in terms of $\frac{dy}{dt}$.

As: $x-1=t$ then $x(t)=t+1$ so $\frac{dx}{dt}=1$
Now: $$y(x(t))'=\frac{dy}{dt}=\frac{dy}{dx}\frac{dx}{dt}=\frac{dy}{dx}\times1=\frac{dy}{dx}$$
Therefore: $$\frac{dy}{dx}=\frac{dy}{dt}$$
