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  • Need solution for RD Sharma maths class 12 chapter 11 Higher Order Derivatives exercise very short answer type question 3

Need solution for RD Sharma maths class 12 chapter 11 Higher Order Derivatives exercise very short answer type question 3

Answers (1)

Answer:

        \frac{d^{2}y}{dx^{2}}=\frac{3}{4t}

Hint:

First diff x w.r.t t, then

\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}} \& \text { hence find } \frac{d^{2} y}{d x^{2}}

Given:

        x=t^{2}\; \; and\; \; y=t^{3}

Explanation:

It is given that

        x=t^{2}\; \; and\; \; y=t^{3}

Diff x w.r.t

        \frac{dy}{dt}=3t^{2}

We know,

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

        \begin{aligned} \frac{d^{2} y}{d x^{2}} &=\frac{3}{2} \frac{d(t)}{d x} \\ &=\frac{3}{2} \frac{d t}{d x} \\ &=\frac{3}{2}\left(\frac{1}{2 t}\right) \\ &=\frac{3}{4 t} \end{aligned}

        \text { Hence, } \frac{d^{2} y}{d x^{2}}=\frac{3}{4 t}

Posted by

Gurleen Kaur

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