\frac{d^2x}{dy^2} equals

Correct Answer is : - (d2ydy2) (dydx)−3

- (\frac{d^2y}{dx^2})^{-1} (\frac{dy}{dx})^{-3}

(\frac{d^2y}{dy^2}) (\frac{dy}{dx})^{-2}

- (\frac{d^2y}{dy^2}) (\frac{dy}{dx})^{-3}

NIMCET 2018 Question Paper with solutions

Question : 19 of 120

Marks: +1, -0

{d^2x}/{dy^2}

equals

Solution:

{dx}/{dy}

({dy}/{dx})^{-1}

Differentiate both sides w.r.t y, we get
⇒

d/{dy}({dx}/{dy})

d/{dy}\{({dy}/{dx})\}^{-1}

⇒

{d^2x}/{dy^2}

d/{dx}\{({dy}/{dx})^{-1}\}

{dx}/{dy}

⇒

{d^2x}/{dy^2}

= -

({dy}/{dx})^{-2}

d/{dx}({dy}/{dx})

({dy}/{dx})^{-1}

⇒

{d^2x}/{dy^2}

= -

({dy}/{dx})^{-3}

({d^2y}/{dx^2})

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