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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 1

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 1

Answers (1)

Answer:

                (b)

Hint:

We must know the derivative of  \cos x and  \sin x .

Given:

                \begin{aligned} &x=a \cos n t-b \sin n t \\\\ &\end{aligned}

Explanation:

                  \begin{aligned} &x=a \cos n t-b \sin n t \\\\ &\end{aligned}

                 \frac{d x}{d t}=a(-\sin n t) \times n-b(\cos n t) \times n \\\\

                \frac{d x}{d t}=-n a \sin n t-n b \cos n t

Differentiate on both sides,

                \begin{aligned} &\frac{d^{2} x}{d t^{2}}=-n a(\cos n t) \times n-n b(-\sin n t) \times n \\\\ \\ \end{aligned}

                \frac{d^{2} x}{d t^{2}}=-n^{2} a(\cos n t)+n^{2} b(\sin n t)

                \frac{d^{2} x}{d t^{2}}=n^{2}[-a \cos n t+b \sin n t] \\\\

                \frac{d^{2} x}{d t^{2}}=-n^{2} x

               

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