Question

if √x+√y =1 then find Dy/dx at (1/4,1/4)​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The value of dy/dx at (1/4,1/4)​ is -1.

Step-by-step explanation:

The given equation is

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

Differentiate with respect to x.

$\dfrac{1}{2\sqrt{x}}+\dfrac{1}{2\sqrt{y}}\cdot \dfrac{dy}{dx}=0$

$\dfrac{1}{2\sqrt{y}}\cdot \dfrac{dy}{dx}=-\dfrac{1}{2\sqrt{x}}$

$\dfrac{dy}{dx}=-\dfrac{2\sqrt{y}}{2\sqrt{x}}$

$\dfrac{dy}{dx}=-\dfrac{\sqrt{y}}{\sqrt{x}}$

Substitute x=1/4 and y=1/4 in the above equation.

$\dfrac{dy}{dx} _{(1/4,1/4)}=-\dfrac{\sqrt{\dfrac{1}{4}}}{\sqrt{\dfrac{1}{4}}}}$

$\dfrac{dy}{dx} _{(1/4,1/4)}=-1$

Therefore, the value of dy/dx at (1/4,1/4)​ is -1.

#Learn more

Y=log (x^2+3), Find dy/dx​.

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