Home
Class 12
MATHS
Let y be an implicit function of x de...

Let `y` be an implicit function of `x` defined by `x^(2x)-2x^xcot y-1=0.` Then `y '(1)` equals: `1` b. `log2` c. `-log2` d. `-1`

A

-1

B

1

C

log 2

D

`-log 2

Text Solution

Verified by Experts

The correct Answer is:
A
`x^(2x)-2x^(x)cot y-1=0" (i)"`
Now at x=1,
`1-2 cot y-1=0rArrcot y =0 rArry=(pi)/(2)`
Now differentiating (i) w.r.t. x, we get
`2x^(2x)(1+log x)-2[x^(x)(-cosec^(2)y)(dy)/(dx)+cot x^(2)(1+log x)]=0`
`"Now at "(1,pi//2)`,
`2(1+log 1)-2[1(-1)((dy)/(dx))_(((1,pi//2)))+0]=0`
`rArr" "2+2((dy)/(dx))_(((1,pi//2)))=0`
`((dy)/(dx))_(((1,pi//2)))=-1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answers Type|3 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Matrix Match Type|1 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Numerical)|41 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let y=f(x) be a function satisfying the differential equation (x d y)/(d x)+2 y=4 x^2 and f(1)=1 . Then f(-3) is equal to

If y is a function of xa n dlog(x+y)-2x y=0, then the value of y^(prime)(0) is (a)1 (b) -1 (c) 2 (d) 0

For relation 2 log y - log x - log ( y-1) =0

If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))_(1,0) is equal to

Write explicit functions of y defined by the following equations and also find the domains of definitions of the given implicit functions: x+|y|=2y (b) e^y-e^(-y)=2x (c) 10^x+10^y=10 (d) x^2-sin^(-1)y=pi/2

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

Find the partial derivatives of the functions at the indicated point G (x,y) = e ^(x+3y) log (x ^(2) + y ^(2)), (-1, 1)

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .

Let y = y(x) be the solution of the differential equation x dy/dx+y=xlog_ex,(xgt1)." If " 2y(2)=log_e4-1," then "y(e) is equal to

The domain of definition of the function y=1/((log)_(10)(1-x))+sqrt(x+2) is

Home
Profile