Question

√x+√y=√10 dy/dx find the derivative of the function

Answer 1

Answer:

- √ y / √ x

Step-by-step explanation:

Given :

√ x + √ y = √ 10

We have to find d y / d x :

Applying chain rule :

Diff. w.r.t. x :

= > 1 / 2 √ x + 1 / 2 √ y . ( y )' = 0

= >  1 / 2 √ y . ( y )' = - 1 / 2 √ x

= >  1 / √ y . ( y )' = - 1 / √ x

= > y' = - √ y / √ x

Hence we get required answer!

Answer 2

Given ,

The function is √x + √y = √10

Differentiating with respect to x , we get

$\sf \mapsto \frac{d \sqrt{x} }{dx} + \frac{d \sqrt{y} }{dx} = \frac{d \sqrt{10} }{dx} \\ \\ \sf \mapsto \frac{1}{2 \sqrt{x} } + \frac{1}{2 \sqrt{y} } \times \frac{dy}{dx} = 0 \\ \\ \sf \mapsto \frac{1}{2 \sqrt{y} } \times \frac{dy}{dx} = - \frac{1}{2 \sqrt{x} } \\ \\ \sf \mapsto \frac{dy}{dx} = - \frac{ \sqrt{y} }{ \sqrt{x} }$

Remmember :

$\sf \star \: \: \frac{d(constant)}{dx} = 0 \\ \\ \star \: \: \sf \frac{d \sqrt{x} }{dx} = \frac{1}{2 \sqrt{x} }$