Implicit Differentiation

IMPLICIT DIFFERENTIATION MOST IMPORTANT MCQ's

1. Find the differentiation of x3 + y3 – 3xy + y2 = 0?

a) (x2−y)x−y2−2y
b) (3x2−3y)3x−3y2−2y
c) (3x3−3y)3x−3y2−2y
d) (3x2−y)3x−3y2−y

2. x3 Sin(y) + Cos(x) y3 = 0, its differentiation is?
a) −[x3Sin(y)−3y2Sin(x)][x2Cos(y)+y3Cos(x)]
b) −[3x2Sin(y)−y3Sin(x)][x3Cos(y)+3y2Cos(x)]
c) −[3x3Sin(y)−y3Sin(x)][x3Cos(y)+3y3Cos(x)]
d) 0

3. Find the differentiation of x4 + y4 = 0.
a) – x3⁄y4
b) – x4⁄y3
c) – x3⁄y3
d) x3⁄y3

4. Find differentiation of xSin(x) + ayCos(x) + Tan(y) = 0.
a) [ayCos(x)−Sin(x)+Cos(x)][aCos(x)+Sec2(y)]
b) [ayCos(x)−Sin(x)+xCos(x)][Cos(x)+Sec2(y)]
c) [ayCos(x)−Sin(x)+xCos(x)][aCos(x)+Sec2(y)]
d) [ayCos(x)−Cos(x)+xCos(x)][aCos(x)+Sec2(y)]

5. Find the derivative of Tan(x) = Tan(y).
a) 1+x21+y2
b) 1+y1+x2
c) 1+y21+x2
d) 1+y21+x

6. Implicit functions are those functions ____________
a) Which can be solved for a single variable
b) Which can not be solved for a single variable
c) Which can be eliminated to give zero
d) Which are rational in nature.

7. Evaluate y44 + 3xy3 + 6x2 y2 – 7y + 8 = 0.
a) (7−12x2y−9xy4−4y3)(3y3+12xy2)
b) (7−12x2y−9xy2−4y3)(3y3+12xy2)
c) (7−12x2y−9xy2−4y3)(3y4+12xy2)
d) (7−12x4y−9xy2−4y3)(3y3+12xy2)

8. If Sin(y)=Sin(-1) (y) then?
a) (1-y2)(1 – Cos2 y) = 1
b) (1-y2)(1 – Sin2 y) = 1
c) (1-y2)(1 – Siny)=1
d) (1-y2)(1 – Cosy)=1

9. If Cos(y)=Cos(-1) (y) then?
a) (1 – y2)(1 – Cos2 (y))=1
b) (1 – y2)(1 – Cos(y))=1
c) (1 – y2)(1 – Sin2 (y))=1
d) (1 – y2)(1 – Sin(y))=1

10. If y2 + xy + x2 – 2x = 0 then d2y⁄dx2 =?
a) (2y+x)d2ydx2+(dydx)2+2dydx+2=0
b) (2y+x)d2ydx2+2(dydx)2+dydx+2=0
c) (2y+x)d2ydx2+2(dydx)2+2dydx+2=0
d) xd2ydx2+2(dydx)2+2dydx+2=0

11. If the velocity of car at time t(sec) is directly proportional to the square of its velocity at time (t-1)(sec). Then find the ratio of acceleration at t=10sec to 9sec if proportionality constant is k=10 sec/mt and velocity at t=9sec is 10 mt/sec.
a) 100
b) 200
c) 150
d) 250

12. If z(x,y) = 2Sin(x)+Cos(y)Sin(x) find d2z(xy)⁄dxdy= ?
a) –Cos(y)Cos(x)
b) -Sin(y)Sin(x)
c) –Sin(y)Cos(x)
d) -Cos(y)Sin(x)

13. If the car is having a displace from point 1 to point 2 in t sec which is given by equation y(x) = x2 + x + 1. Then?
a) Car is moving with constant acceleration
b) Car is moving with constant velocity
c) Neither acceleration nor velocity is constant
d) Both acceleration and velocity is constant