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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 13

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 13

Answers (1)

Answer:

                (a)

Hint:

We must know about the derivative of x

Given:

                x=2 a t, y=a t^{2} \\ , where  a  is constant.

Explanation:

                x=2 a t, y=a t^{2} \\

                \frac{d x}{d t}=2 a, \frac{d y}{d t}=2 a t \\

                \begin{aligned} &\frac{d y}{\frac{d t}{d x}}{d t}=\frac{2 a t}{2 a} \end{aligned}

                =t \\

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

                \begin{aligned} & &\frac{d^{2} y}{d x^{2}}=\frac{d}{d t}\left(\frac{d y}{d x}\right) \frac{d t}{d x} \end{aligned}

                =\frac{d}{d t}(t) \frac{d t}{d x} \\

                =1\left(\frac{1}{2 a}\right) \\

                \begin{aligned} &=\frac{1}{2 a} \end{aligned}

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