Differentiate w.r.t. time. (i) `y=t^(2) " "` (ii) `x=t^(3//2)" "` (iii) `y=(1)/(sqrt(t))`
(iv) `x=4t^(3) " "` (v) `y=2sqrt(t) " "` (vi) `y=2t^(2)+t-1`
(vii)`y=3sqrt(t)+(2)/(sqrt(t))` (viii) `y=t^(3)sin t " "` (ix) `x=te^(t)`
(x) `x= sqrt(t)(1-t)`

Explanation

(i) `(dy)/(dt)=2t " " ` (ii) `(dx)/(dt)=(3)/(2)t^(1//2)" "` (iii) `(dy)/(dx)=-(1)/(2)t^(-3//2)`
(iv) `(dx)/(dt)=12t^(2) " "` (v) `(dy)/(dt)=2((1)/(2)t^(-1//2))=t^(-1//2)`
(vi)`(dy)/(dt)=4t+1+0=4t+1 " " `(vii) `(dy)/(dt)=3((1)/(2)t^(-1//2))+2(-(1)/(2)t^(-3//2))`
`=(3)(2sqrt(t))-t^(-3//2)`
(viii) `(dy)/(dt)=3t^(2)sin" "t+t^(3) cos" "t " "` (ix) `(dx)/(dt)=e^(1)+te^(t)=e^(t)=e^(t)(1+t)`
(x) `(dx)/(dt)=(1)/(2)t^(-1//2)-(3)/(2)t^(1//2)=(1)/(2sqrt(t))-(3)/(2)sqrt(t)`