hi im currently stuck on a problem
df/dx=3x^2+2xy df/dy=x^2+2y+2 x(t)=sqrt 1+t^2 y(t)=-t dx/dt=t/sqrt 1+t^2 dy/dt= -1
now i have to use the chain rule df/dt=df/dx x dx/dt + df/dy x dy/dt
df/dt=(3x^2+2xy)(t/sqrt 1+t^2)+(x^2+2y+2)(-1)
Now substitute x = sqrt(1 + t^2), y = -t into df/dt
have i done all this correct so far , and can any one show me step by step how to finish it all , thanks.
df/dx=3x^2+2xy df/dy=x^2+2y+2 x(t)=sqrt 1+t^2 y(t)=-t dx/dt=t/sqrt 1+t^2 dy/dt= -1
now i have to use the chain rule df/dt=df/dx x dx/dt + df/dy x dy/dt
df/dt=(3x^2+2xy)(t/sqrt 1+t^2)+(x^2+2y+2)(-1)
Now substitute x = sqrt(1 + t^2), y = -t into df/dt
have i done all this correct so far , and can any one show me step by step how to finish it all , thanks.