If y - -x - 1-x- then show that 2xdydx - y - 2-x

y = √(x)+1√(x) dydx = 12√(x)+ 12√(x)x = 12√(x) 12x√(x) 2xdydx = 2x(12√(x) 12x√(x)) = 2(√(x)2 12√(x)) = √(x) 1√(x) ∴ 2xdydx+y = √ ...

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Implicit Differentiation

If y = √x +...

Question

If $y = \sqrt{x} + \frac{1}{\sqrt{x}},$ then show that $2 x \frac{d y}{d x} + y = 2 \sqrt{x}$

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

2 x \frac{d y}{d x} + y = 2 \sqrt{x}

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

2 x \frac{d y}{d x} + y = 2 \sqrt{x} .

y = \sqrt{x} - \frac{1}{\sqrt{x}}

2 x \frac{d y}{d x} + y

y = ({sin}^{- 1} x)^{2}

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

If $\sqrt{1 - x^{2}} + \sqrt{1 - y^{2}} = a (x - y)$ , then show that $\frac{d y}{d x} = \sqrt{\frac{1 - y^{2}}{1 - x^{2}} . d x}$

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