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

Textbook Question

Chapter 3, 3.5 - Problem 6 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

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)

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balajia | College Teacher | (Level 1) eNoter

Posted on

`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))`

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