If and y = f(t) t + f'(t) t,

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If x=f(t)cos⁡t−f′(t)sin⁡tx = f(t) \cos t - f'(t) \sin t and y=f(t)sin⁡t+f′(t)cos⁡t,y = f(t) \sin t + f'(t) \cos t,  then (dxdt)2+(dydt)2 is equal to\text{ then } \left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 \text{ is equal to} (1) f(t)−f′′(t)f(t) - f''(t) (2) [f(t)−f′′(t)]2[f(t) - f''(t)]^2 (3) [f(t)+f′′(t)]2[f(t) + f''(t)]^2 (4) None of these

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