# 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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