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we are given that dy/dx = x/y. Find an expression d^2y/dx^2 in terms of x and y

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babbieleo40

   

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Answer:

[tex]{ \rm{ \frac{dy}{dx} = \frac{x}{y} }} \\ \\ { \boxed{ \blue{ \tt{ \frac{ {d}^{2}y }{dx {}^{2} } = \frac{d}{dx} ( \frac{dy}{dx} })}}} \\ \\{ \boxed{ \blue{ \tt{from \: quotient \: rule : }}}} \\ \\ { \rm{ \frac{ {d}^{2}y }{dx {}^{2} } = \frac{y - x \frac{dy}{dx} }{ {y}^{2} } }} \\ \\ { \rm{ \frac{ {d}^{2} y}{dx {}^{2} } = \frac{y - (x \times \frac{x}{y} )}{ {y}^{2} } }} \\ \\ { \boxed{ \boxed{ \rm{ \frac{ {d}^{2} y}{dx {}^{2} } = \frac{y {}^{2} - { {x}^{2} }}{ {y}^{3} } }}}}[/tex]

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