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  • Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 5

Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 5

Answers (1)

Answer:

                (b)

Hint:

We must know the derivative of x and  y

Given:

                x=t^{2}, y=t^{3}

Explanation:

                 x=t^{2}, y=t^{3}

                \begin{aligned} &\frac{d x}{d t}=2 t, \frac{d y}{d t}=3 t^{2} \\ \end{aligned}

               \frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{3 t^{2}}{2 t} \\

               =\frac{3}{2} t

Differentiate on both sides,

                \begin{aligned} &\frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left(\frac{3}{2} t\right) \\ & \end{aligned}

               =\frac{d}{d t}\left(\frac{3}{2} t\right) \times \frac{d t}{d x} \\

               =\frac{3}{2} t^{2} \times \frac{1}{2 t} \\

               =\frac{3}{4} t

 

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