If `y=sin^(-1)(x-y),x=3t,y=4t^(3)`, then what is the derivative of u with respect to t?A. `3(1-t^(2))`B. `3(1-t^(2))^(-(1)/(2))`C. `5(1-t^(2))^((1)/(2))`D. `5(1-t^(2))`

If `y=sin^(-1)(x-y),x=3t,y=4t^(3)`, then what is the derivative of u w

1.	If `y=sin^(-1)(x-y),x=3t,y=4t^(3)`, then what is the derivative of u with respect to t?A. `3(1-t^(2))`B. `3(1-t^(2))^(-(1)/(2))`C. `5(1-t^(2))^((1)/(2))`D. `5(1-t^(2))`
Answer» Correct Answer - B `u=sin^(-1)(x-y)x=3t,y=4t^(3)` So, `u=sin^(-1)(3t-4t^(3))` Let `t=sin theta rArr theta=sin^(-1)t`, So, `u=sin^(-1)(3sin theta-4sin^(3)theta)` `=sin^(-1)(sin3theta)=3 theta` Hence, `u=3sin^(-1)t` `(du)/(dt)=3(1)/(sqrt(1-t^(2)))=3(1-t^(2))^(-1//2)`