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Problem If x = f ( t ) cos t − f ′ ( t ) sin t x = f(t) \cos t - f'(t) \sin t x = f ( t ) cos t − f ′ ( t ) sin t y = f ( t ) sin t + f ′ ( t ) cos t , y = f(t) \sin t + f'(t) \cos t, y = f ( t ) sin t + f ′ ( t ) cos t , then ( d x d t ) 2 + ( d y d t ) 2 is equal to \text{ then } \left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 \text{ is equal to} then ( d t d x ) 2 + ( d t d y ) 2 is equal to f ( t ) − f ′ ′ ( t ) f(t) - f''(t) f ( t ) − f ′′ ( t ) [ f ( t ) − f ′ ′ ( t ) ] 2 [f(t) - f''(t)]^2 [ f ( t ) − f ′′ ( t ) ] 2 [ f ( t ) + f ′ ′ ( t ) ] 2 [f(t) + f''(t)]^2 [ f ( t ) + f ′′ ( t ) ] 2 Browse the problem library