Question

If root xy=1, then dy/dx​

Answer 1

Answer:Hello,

If xy = 1 then

y = 1/x

Thus:

dy/dx = -1/x²

And

y² + dy/dx = (1/x)² + (-1/x²) = 1/x² – 1/x² = 0

Step-by-step explanation:mark as brainliest

Answer 2

Answer:

the value of $\frac{dy}{dx}=-\frac{1}{x^2}$  when $\sqrt{xy}=1$

Step-by-step explanation:

Given:

Since we are given the expression

$\sqrt {xy }=1$

To Find :

Derivative of the above expression

Solution :

Since we have to find the derivative of the above expression

$\sqrt{xy}=1$

Squaring both sides of the equation

$(\sqrt{xy})^2=1^2$

$\implies$ xy = 1

$y = \frac{1}x$

taking derivatives both sides

$\frac{d}{dx}y=\frac{d}{dx}(\frac{1}{x})$

$\frac{dy}{dx}= \frac{d}{dx}x^{-1}$

since we know that $\frac{d}{dx}x^n=nx^{n-1}$

$\frac{dy}{dx}=(-1)x^{-1-1$

$\frac{dy}{dx}=(-1)x^{-2$

$\frac{dy}{dx}=-x^{-2}$

$\frac{dy}{dx}=-\frac{1}{x^2}$

Hence we get the value of $\frac{dy}{dx}=-\frac{1}{x^2}$

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