JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

x=f(t) \cos t-f^{\prime}(t) \sin t

and

y=f(t) \sin t+f^{\prime}(t) \cos t

, then

\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2

is equal to

View answer and explanation

Correct option: C

\left[f(t)+f^{\prime \prime}(t)\right]^2

Option C ([f(t)+f''(t)]²) is correct because it is the result of calculating the derivatives and simplifying the expression.

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