Find `dy/dx` in terms of x and y if `(x)^(1/4)=2*sqrt(y)` .

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is given that `(x)^(1/4) = 2*sqrt y` . To determine `dy/dx` use implicit differentiation

`(1/4)*x^(-3/4) = 2*(1/2)*y^(-1/2)*(dy/dx)`

=> `dy/dx = x^(-3/4)*y^(1/2)/4`

The required derivative `dy/dx = sqrt y/(4*x*sqrt x)`

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hattielee | Student | (Level 1) eNoter

Posted on

from (x)^(1/4)=2*sqrt(y)

we get y=(1/4)(x)^(1/2)

y'=(1/4)*(1/2)(x)^(-1/2)

So dy/dx=1/(8*sqrt(x))

 

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