# `2sqrt(x) + sqrt(y) = 3` Find `(dy/dx)` by implicit differentiation.

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### 2 Answers

*Note:- 1) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number*

*2) If y = k ; where 'k' = constant ; then dy/dx = 0*

Now,

{2x^(1/2)} + y^(1/2) = 3

Differentiating both sides w.r.t 'x' we get

*x^(-1/2) + (1/2){y^(-1/2)}*(dy/dx) = 0*

*or, dy/dx = -[2* x^(-1/2)]/[y^(-1/2)]*

*or, dy/dx = -2[x/y]^(-1/2) = -2*[y/x]^(1/2)*

### User Comments

`2sqrt(x)+sqrt(y)=3`

differentiating with respect to x.

`2(1/(2sqrt(x)))+(1/(2sqrt(y)))(dy/dx)=0`

`dy/dx=(-(2sqrt(y))/sqrt(x))`