Calculus

Calculus of Parametric Equations

Parametric Equations - Derivative

         

If x=t3x = t^3 and y=3t5y = 3t^5, where tt is any real number, what is the derivative of yy with respect to xx at x=216x = 216?

What is the equation of the tangent line to the curve x=14sint,y=5 sin(t+sint)x = 14 \sin t, y = 5\ \sin(t + \sin t) at (0,0)(0,0)?

If x=lntx = \ln t and y=3t3+9lnty = 3 t^3 + 9 \ln t what is dydx?\displaystyle{\frac{d y}{d x}}?

If x=t+1tx=t+\frac{1}{t} and y=t2+1t2y=t^2+\frac{1}{t^2}, what is the derivative of yy with respect to xx at x=21x=21?

At time tt, the coordinates of a point PP are given by (4cost,2sint) (4 \cos t, 2 \sin t) . At time t=π4t=\frac{\pi}{4}, the magnitudes of velocity and acceleration are mm and nn, respectively. What is m2+n2m^2+n^2?

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