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.
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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 $\displaystyle c(t) = (x(t),y(t),z(x,y)) = (7t + 6, 9t^2 + 6t, (7t + 6)^2 + \sin [(7t + 6)(9t^2 + 6t)])$? just differentiate the components, your vector is $\displaystyle \left< x'(t), y'(t), z'(t) \right>$
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