A Particle in \(x\)-\(y\) plane

A particle is moving on a curve whose position at any time \(t\) is given by \(x(t)=f'(t)\sin(t)+f''(t)\cos(t)\), \(y(t)=f'(t)\cos(t)-f''(t)\sin(t)\).

where \(f(x)\) is a thrice differentiable function. Then the speed of the particle at time \(t\) is given by:

A)\(\left| f'(t)+f'''(t) \right| \)

B)\(\left| f'''(t) \right| \)

C)\(\left| f''(t)+f'(t) \right| \)

D)\(\left| f'(t)-f'''(t) \right| \)


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