# Math Help - Calc III Partial Derivatives

1. ## Calc III Partial Derivatives

Find the tangent vector to the curve c(t)= (g(t),h(t), f(g(t),h(t))) on the surface z= f(x,y)=x^2+sin(xy) when t=1, and where x=7t+6 and y=9t^2+6t.

2. Originally Posted by Snooks02
Find the tangent vector to the curve c(t)= (g(t),h(t), f(g(t),h(t))) on the surface z= f(x,y)=x^2+sin(xy) when t=1, and where x=7t+6 and y=9t^2+6t.
so you want the tangent vector for
$c(t) = (x(t),y(t),z(x,y)) = (7t + 6, 9t^2 + 6t, (7t + 6)^2 + \sin [(7t + 6)(9t^2 + 6t)])$?

just differentiate the components, your vector is $\left< x'(t), y'(t), z'(t) \right>$