Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Differentiation

BITSAT 2020 · Mathematics · Differentiation

If x y+y^ 2 = x+y, then find (d y)/(d x) is

If xy+y2=tan⁡x+y,x y+y^{2}=\tan x+y, then find dydx\frac{d y}{d x} is

Options

  1. Asec⁡2xx+2y\frac{\sec ^{2} x}{x+2 y}
  2. Bsec⁡2x−y(x+2y−1)\frac{\sec ^{2} x-y}{(x+2 y-1)}
  3. C(x+2y−1)sec⁡2x(x+2 y-1) \sec ^{2} x
  4. Dsec⁡2x⋅y\sec ^{2} x \cdot y

Correct answer

B. sec⁡2x−y(x+2y−1)\frac{\sec ^{2} x-y}{(x+2 y-1)}

Step-by-step solution

The given relation is xy+y2=tan⁡x+yx y+y^{2}=\tan x+y. Differentiating both sides with respect to xx, we get ddx(xy)+ddx(y2)=ddx(tan⁡x)+dydxor[y⋅1+x⋅dydx]+2ydydx=sec⁡2x+dydxor(x+2y−1)dydx=sec⁡2x−y∴dydx=sec⁡2x−y(x+2y−1)\frac{d}{d x}(x y)+\frac{d}{d x}\left(y^{2}\right)=\frac{d}{d x}(\tan x)+\frac{d y}{d x} or \left[y \cdot 1+x \cdot \frac{d y}{d x}\right]+2 y \frac{d y}{d x}=\sec ^{2} x+\frac{d y}{d x} or (x+2 y-1) \frac{d y}{d x}=\sec ^{2} x-y\therefore \frac{d y}{d x}=\frac{\sec ^{2} x-y}{(x+2 y-1)}
Practice Differentiation on Quantrex Academy →

More from Differentiation

If x 1+y +y 1+x =0 , then (d y)/(d x)= BITSAT 2024If y= ^ -1 ( x -x 1+x^ (3)/(2) ), then y^ (1) is equal to BITSAT 2024At x=(π^2)/(4), (d)/(d x)( ^ -1 ( x )+ ^ -1 (e^x))= BITSAT 2024The slope of the tangent to the curve x=3 t^2+1 , y=t^3-1 at x=1 is: BITSAT 2023If y^x=e^ y-x , then (d y)/(d x) is equal to BITSAT 2023If f(x)= 1+ ^2(x^2) , then the value of f^ ( π 2 ) BITSAT 2023The derivative of e^ x^3 with respect to x is BITSAT 2023If y= ((1+ 2 θ)/(1- 2 θ)) , then (d y)/(d θ) at θ=(3 π)/(4) is : BITSAT 2023If 2^ x +2^ y =2^ x+y , then (d y)/(d x)= BITSAT 2021If x= 1-t^ 2 1+t^ 2 and y= 2 t 1+t^ 2 , then (d y)/(d x) is equal to : BITSAT 2021(d)/(d x) ( ^ -1 (1+ (x)/(2))/(1- (x)/(2)) ) is equal to BITSAT 2021Let f ( x ) = x [x], x ∉ Z , ( [ · ] denotes greatest integer function), then f^ ' (x) is… BITSAT 2019If g is the inverse of function f and f^ (x)= x , then ^ (x) is equal to BITSAT 2015If y=1+x+ x^ 2 2 ! + x^ 3 3 ! +…. ∞, then (d y)/(d x) is equal to BITSAT 2013Let f(x+y)=f(x) · f(y) for all x, y where f(0) ≠ 0 If f(5)=2 and f^ (0)=3, then f^ (5) is… BITSAT 2012If x=a θ and y=b θ, then d^ 2 y d x^ 2 is BITSAT 2012 Full Differentiation list Differentiation JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs