If y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+...

If `y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+x^2)/(1-x^2))` , `x >0` , prove that `(dy)/(dx)=4/(1+x^2)` .

Text Solution

AI Generated Solution

Topper's Solved these Questions

DIFFERENTIALS, ERRORS AND APPROXIMATIONS
RD SHARMA ENGLISH|Exercise All Questions|107 Videos
DIRECTION COSINES AND DIRECTION RATIOS
RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If y= sin^(-1)((2x)/(1+x^2)) + sec^(-1)((1+x^2)/(1-x^2)) , prove that (dy)/(dx)=4/(1+x^2) .

If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)),0ltxlt1, prove that (dy)/ (dx)="4/(1+x^2)

If y= sin^(-1)((2x)/(x^(2)+1)) +sec^(-1)((1+x^(2))/(1-x^(2))) , prove that (dy)/(dx)=(4)/(1+x^(2)) .

If y= "tan"^(-1) (2x)/(1-x^(2)) , prove that (dy)/(dx)= (2)/(1 + x^(2))

If y= sin^(-1)(x/(sqrt(1+x^2))) + cos^(-1)(1/(sqrt(1+x^2))) , prove that (dy)/(dx)=(2x)/(1+x^2) .

If y= "tan"^(-1) (4x)/(1+5x^(2)) + "tan"^(-1) (2 + 3x)/(3-2x) , then prove that (dy)/(dx)= (5)/(1+25x^(2))

sec^-1((1+tan ^2x)/(1-tan ^2 x))

If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xdot

If y=x\ sin^(-1)x+sqrt(1-x^2) , prove that (dy)/(dx)=sin^(-1)x

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions

Differentiate cot^(-1)((1-x)/(1+x)) with respect to x .
Text Solution
|
If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]...
Text Solution
|
If y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+x^2)/(1-x^2)) , x >0 , prove t...
Text Solution
|
If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...
Text Solution
|
If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)
Text Solution
|
If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),\ \ \ x \ \ is \ [0,1/2] , fi...
Text Solution
|
If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0 , prove ...
Text Solution
|
If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2) ,x is [-1/2,0] , find (dy)/(dx...
Text Solution
|
If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...
Text Solution
|
If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)
Text Solution
|
Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...
Text Solution
|
If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) .
Text Solution
|
If x^2+2x y+y^3=42 , find (dy)/(dx)
Text Solution
|
If x^3+y^3=3a x y , find (dy)/(dx)
Text Solution
|
If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x...
Text Solution
|
Find dy/dx if x=sqrt(1+y)
Text Solution
|
If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...
Text Solution
|
If siny=xsin(a+y), prove that (dy)/(dx)= (sin^2(a+y))/(sina) .
Text Solution
|
If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),prove that (dy)/(dx)=(x^2)/(y^2...
Text Solution
|
If x^2+y^2=t-1/t and x^4+y^4=t^2+1/(t^2) , then prove that (dy)/(dx)=1...
Text Solution
|