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  • Find   <img alt="\frac{d^2 y}{d x^2} \text { if } x^2+y^2=6" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7Bd%5E2%20y%7D%7Bd%20x%5E2%7D%20%5Ctext%20%7B%20if%20%7D%20x%5E2&

Find   \frac{d^2 y}{d x^2} \text { if } x^2+y^2=6

Option: 1

\text { }-\frac{4}{y^3}


Option: 2

-\frac{5}{y^3}


Option: 3

-\frac{6}{y^3}


Option: 4

-\frac{7}{y^3}


Answers (1)

best_answer

On differentiating, we get

\frac{dy}{dx}=-\frac{x}{y}

Hence by quotient rule,

\begin{aligned} & \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=-\frac{d}{\mathrm{~d} x}\left(\frac{x}{y}\right) \\ & =-\frac{y-x \frac{d y}{d x}}{y^2} \\ & =-\frac{y-x \frac{-x}{y}}{y^2} \\ & =-\frac{y^2+x^2}{y^3} \\ & =-\frac{6}{y^3} \end{aligned}

Posted by

Divya Prakash Singh

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