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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 14

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 14

Answers (1)

Answer:

                (a)

Hint:

We must know about the derivative.

Given:

                x=f(t), y=g(t)

Explanation:

                x=f(t), y=g(t)

                \\ \frac{d x}{d t}=f^{\prime}(t), \frac{d y}{d t}=g^{\prime}(t) \

                \ \frac{d y}{dt}\cdot{\frac{d t}{d x}}=\frac{g^{\prime}(t)}{f^{\prime}(t)} \\

                \begin{aligned} &\frac{d y}{d x}=\frac{g^{\prime}(t)}{f^{\prime}(t)} \end{aligned}

Differentiate on both sides,

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

                =\frac{d}{d t}\left(\frac{g^{\prime}(t)}{f^{\prime}(t)}\right) \times \frac{d t}{d x} \\

                =\frac{f^{\prime}(t) g^{\prime \prime}(t)-g^{\prime}(t) f^{\prime \prime}(t)}{\left(f^{\prime}(t)\right)^{2}} \times \frac{1}{f^{\prime}(t)}

                =\frac{f^{\prime}(t) g^{\prime \prime}(t)-g^{\prime}(t) f^{\prime \prime}(t)}{\left(f^{\prime}(t)\right)^{3}}

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