If sqrt{frac{y}{x}}+4 sqrt{frac{x}{y}}=4, the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given equation is $\sqrt{\frac{y}{x}}+4 \sqrt{\frac{x}{y}}=4$.Let $u = \sqrt{\frac{y}{x}}$. Then the equation becomes $u + \frac{4}{u} = 4$.Multip

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given equation is $\sqrt{\frac{y}{x}}+4 \sqrt{\frac{x}{y}}=4$.Let $u = \sqrt{\frac{y}{x}}$. Then the equation becomes $u + \frac{4}{u} = 4$.Multiplying by $u$, we get $u^2 - 4u + 4 = 0$, which is $(u-2)^2 = 0$.Thus, $u = 2$, which implies $\sqrt{\frac{y}{x}} = 2$.Squaring both sides, we get $\frac{y}{x} = 4$, or $y = 4x$.Now, differentiating both sides with respect to $x$, we get $\frac{d y}{d x} = \frac{d}{d x}(4x) = 4$.Therefore, $\frac{d y}{d x} = 4$.

If $\sqrt{\frac{y}{x}}+4 \sqrt{\frac{x}{y}}=4$, then $\frac{d y}{d x}=$

Similar Questions

If $2 x^2-3 x y+y^2+x+2 y-8=0$,then $\frac{d y}{d x}$ is equal to

Find $\frac{dy}{dx}$ for the function $x^{y} + y^{x} = 1$.

If $3 \sin xy + 4 \cos xy = 5$,then $\frac{dy}{dx}$ is equal to . . . . . .

If $(x e)^{y}=e^{x}$,then $\frac{d y}{d x}$ is

If $f(x)$ is an invertible and twice differentiable function satisfying $f'(x) = \int_{0}^{f(x)} f^{-1}(t) dt$ for all $x \in R$ and $f'(0) = 1$,then $f'(1)$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module