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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 2

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 2

Answers (1)

Answer:

                (d)

Hint:

We must know about the derivative of  t .

Given:

                x=a t^{2}, y=2 a t

 

Explanation:

                 x=a t^{2}

                 \Rightarrow \quad \frac{d x}{d t}=2 a t

                 y=2 a t

                 \Rightarrow \frac{d y}{d t}=2 a

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

               \Rightarrow \frac{d y}{d x}=\frac{1}{t}

Differentiate on both sides,

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

                =\frac{d}{d t}\left(\frac{d y}{d x}\right) \times \frac{d t}{d x}

                \begin{aligned} &=\frac{d}{d t}\left(\frac{1}{t}\right) \times \frac{1}{2 a t} \\ \end{aligned}

                =\frac{-1}{t^{2}} \times \frac{1}{2 a t} \\

                =\frac{-1}{2 a t^{3}}

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