Question

Find dx/dt by implicit differentiation. x-sqrt(t)=tx

Answer 1

Dx/dt- (1/2)t^(-1/2) = t*dx/dt + x*1

dx/dt- t*dx/dt= x + (1/2)t^(-1/2)

Dx/dt(1-t)= x+(1/2)t^(-1/2)

Dx/dt= [x+(1/2)t^(-1/2)]/ (1-t)

then multiply by 2t^(1/2)

= [2xt^(1/2)+1]/ [2t^(1/2) -2t^(3/2)]