Let y=ex+ex+ex+…… , then which of the following is not equal to dydx?

y2=ex+y y'=ex2y−1=y2−y2y−1 y2−y−ex=0 y=1+1+4ex2⇒2y−1=1+4ex

Let y=ex+ex+ex+…… , then which of the following is not equal to dydx?

y2=ex+y y'=ex2y−1=y2−y2y−1 y2−y−ex=0 y=1+1+4ex2⇒2y−1=1+4ex

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Let $y = \sqrt{e^{x} + \sqrt{e^{x} + \sqrt{e^{x} + \dots \dots}}}$ , then which of the following is not equal to $\frac{d y}{d x} ?$

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$\frac{e^{x}}{2 y - 1}$

$\frac{- e^{x}}{\sqrt{1 + 4 e^{x}}}$

$\frac{e^{x}}{\sqrt{1 + 4 e^{x}}}$

$\frac{y^{2} - y}{(2 y - 1)}$

answer is D.

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$y^{2} = e^{x} + y y' = \frac{e^{x}}{2 y - 1} = \frac{y^{2} - y}{2 y - 1} y^{2} - y - e^{x} = 0 y = \frac{1 + \sqrt{1 + 4 e^{x}}}{2} \Rightarrow 2 y - 1 = \sqrt{1 + 4 e^{x}}$

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Let y=ex+ex+ex+…… , then which of the following is not equal to dydx?

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Let $y = \sqrt{e^{x} + \sqrt{e^{x} + \sqrt{e^{x} + \dots \dots}}}$ , then which of the following is not equal to $\frac{d y}{d x} ?$