The derivative of the function represented parametrically as `x=2t=|t|,y=t^3+t^2|t|a tt=0` is a. -1 b. 1 c. 0 d. does not exist

Find the derivative of the function g(t) = t^(3) cos t

Find the derivative of the function g(t) = ((t-2)/(2t+1)) .

Area enclosed by the curve y=f(x) defined parametrically as x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2) is equal

A curve is represented parametrically by the equations x=t+e^(at) and y=-t+e^(at) when t in R and a > 0. If the curve touches the axis of x at the point A, then the coordinates of the point A are

A curve is represented parametrically by the equations x=f(t)=a^(In(b^t))and y=g(t)=b^(-In(a^(t)))a,bgt0 and a ne 1, b ne 1" Where "t in R. The value of (d^(2)y)/(dx^(2)) at the point where f(t)=g(t) is

The equation of the normal to the curve parametrically represented by x=t^(2)+3t-8 and y=2t^(2)-2t-5 at the point P(2,-1) is

The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^2+t+1; t in R , is (1, 1) (b) (2, 2) (1/2,1/2) (d) (3,3)

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

A curve is represented parametrically by the equations x=f(t)=a^(In(b'))and y=g(t)=b^(-In(a^(t)))a,bgt0 and a ne 1, b ne 1" Where "t in R. The value of f(t)/(f'(t))cdot(f''(-t))/(f'(-t))+(f(-t))/(f'(-t))cdot(f''(t))/(f'(t))AA t in R is