"Second derivatives Find d2ydx2.x+y2=1" was answered by students like you

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Answered question

2021-10-10

Second derivatives Find

d^{2} \frac{y}{{d x}^{2}} . x + y^{2} = 1

Answer & Explanation

Willie

Skilled2021-10-11Added 95 answers

Given,

x + y^{2} = 1

Differentiating with respect to x, we get

1 + 2 y \cdot \frac{d y}{d x} = 0

\Rightarrow 2 y \cdot \frac{d y}{d x} = - 1

\Rightarrow \frac{d y}{d x} = - \frac{1}{2 y}

Again differentiating with respect to x, we get

\frac{d^{2} y}{{d x}^{2}} = - \frac{1}{2} \cdot (- \frac{1}{y^{2}} \cdot \frac{d y}{d x}) [∵ \frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x^{2}}]

= \frac{1}{2 y^{2}} (- \frac{1}{2 y}) [∵ \frac{d y}{d x} = - \frac{1}{2 y}]

= - \frac{1}{4 y^{3}}

Jeffrey Jordon

Expert2021-11-19Added 2605 answers

Answer is given below (on video)

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