Like dx/dy=1/dy/dx d^2x/dy^2=-(d^2y/dx^2).(dy/dx)^-3 d^3x/dy^3=-((dy/dx).(d^3y/dx^3)-3(d^2y/dx^2)^2)/(dy/dx)^5 What is d^4x/dy^4 and also what is d^5x/dy^5

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y = f (x)

\frac{d^{2} x}{d y^{2}} = - {(\frac{d y}{d x})}^{- 3} \frac{d^{2} y}{d x^{2}}

\frac{d^{2} y}{d x^{2}} {(\frac{d x}{d y})}^{3} + \frac{d^{2} x}{d y^{2}}

y = 1 + {(\frac{d y}{d x})}^{1} + \frac{1}{2!} {(\frac{d y}{d x})}^{2} + \frac{1}{3!} {(\frac{d y}{d x})}^{3} + . . . . .

\frac{d^{2} y}{d x^{2}} = x l o g (\frac{d y}{d x})

\frac{d y}{d x} + y = \frac{1}{\frac{d y}{d x}}

_{e} [\frac{d y}{d x} - \frac{d^{3} y}{d x^{3}}] = l n [\frac{d^{5} y}{d x^{5}} + 1]

{[(\frac{d y}{d x})^{1 / 3} + y]}^{2} = \frac{d^{2} y}{d x^{2}}

\frac{d^{2} x}{d y^{2}} e q u a l s

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