# Calc III Partial Derivatives

• Sep 17th 2008, 06:43 PM
Snooks02
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.
• Sep 17th 2008, 07:03 PM
Jhevon
Quote:

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 $\left< x'(t), y'(t), z'(t) \right>$