Home
Class 12
MATHS
"If "sqrt(x)+sqrt(y)=4," then find "(dy)...

`"If "sqrt(x)+sqrt(y)=4," then find "(dy)/(dx).`

Text Solution

Verified by Experts

We have `sqrt(x)+sqrt(y)=4`
Differentiating the given equation both sides w.r.t.x, we get
`(1)/(2sqrt(x))+(d)/(dx)(sqrt(y))=0`
`rArr(1)/(2sqrt(x))+((d)/(dy)(sqrt(y)))(dy)/(dx)=0`
`rArr(1)/(2sqrt(x))+(1)/(2sqrt(y))cdot(dy)/(dx)=0`
`rArr(dy)/(dx)=-(sqrt(y))/(sqrt(x))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If y=sqrt(sinx+y) , then find (dy)/(dx)

If y=e^(sqrt(x))-e^(-sqrt(x))," then "(dy)/(dx) is equal to

If y=sqrt(x+bx^2) , then find dy/dx

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to -

If sqrt(x) + sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

"if "y=sin^(-1)[sqrt(x)sqrt(1-x^(2))-x sqrt(1-x)] and 0lt x lt 1," then find "(dy)/(dx).

y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] then find dy/dx

If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)), then find= (dy)/(dx)

If y=sqrt(sin sqrt(x)) , then the value of (dy)/(dx) is -

If y=sin^(-1)(sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)