Let $c(t) = (t^3, t^2, 2t)$ and $f(x,y,z)=(x^2-y^2, 2xy, z^2).$
(a) Find $(f\circ c)(t)$
(b) Find a parametrization for the tangent line to the curve $f\circ c$ at $t=1$.
I know how to find the tangent line ($L(c) = c(t_0) +(t-t_0)(c\prime t_0))$, however I need help with the function composition.
By function composition, $f\cdot c = ((t^3)^2 - (t^2)^2, 2(t^3)(t^2), (2t)^2) = (t^6 - t^4, 2t^5, 4t^2)$.