Find the derivative of $$f(x,y)= x^2 + y^2$$ in the direction of the unit tangent vector of curve $$r(t) = (cos(t)+tsin(t))i + (sin(t)-cos(t))j$$
gradient of f is $$2xi+2yj$$
$$d/dt ((cos(t)+tsin(t)) = tcost$$ $$d/dt((sin(t)-cos(t)) = tsint$$ norm of u = $$\sqrt{((tcost)^2)+((tsint)^2))}$$ $$=\sqrt{(t^2cos^2t+t^2sin^2t)}$$ $$=\sqrt{(t^2(cos^2t+sin^2t))}$$ $$=\sqrt{(t^2(1))=sqrt(t^2)}$$ $$=t$$
u = dr/dt = $$\frac{(tcosti+tsintj)}{(\sqrt{((tcost)^2)+((tsint)^2))})}$$
$$= costi+sintj$$
grad * u = ?
Correct answer is 2