Find `(dx)/(dt)` (derivation of x with respect to t)
(i) `x=(t^(2)+1)^(3) " "` (ii) `x=sin2t`

Find (dx)/(dt) (derivative) of w.r.t. t). (i) x=(t^(2)+1)^(3) (ii) x=sqrt(t)^(3)-3 (iii) x=sin2t (iv) x=cos(2t+4) (v) x=sin^(3)t (vi) x=cos^(3)t

Find the derivative of the following with respect to x. (i) int_(0)^(x) cos t dt (ii) int_(0)^(x^(2)) cos^(2) dt

Find the derivative of the following with respect to x. (i) int_(0)^(x) cos t dt (ii) int_(0)^(x^(2)) cos^(2) dt

Find the derivative of the following with respect to x. (i) int_(0)^(x) cos t dt (ii) int_(0)^(x^(2)) cos^(2) dt

If u=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)

Find derivative of sin(x^(2)) w.r.t.to x

Find the derivative with respect to x of the following functions : (a) F(x) = int_(0)^(2x) (sin t)/(t) dt , (b) f(x) = int_(x)^(0) sqrt(1 + t^(4)) dt

Find (dx)/(dt) when x = sin^-1(t.sqrt(1-t) +sqrt(t) sqrt(1-t^2)) .

Evaluate indefinite integration. (i) x=intdt " " (ii) int t dt " " (iii) x=int (2t) dt" " (iv) x=int (t^(2)) dt " " (v) x=int (-(2)/(t^3))dt

Find the derivatives of the following functions : (a) F (x) = int_(1)^(x) " In t dt " (x gt 0) (b) F (x) = int_(2//x)^(x^(2)) (dt)/(t)