Home
Class 12
MATHS
If y=tan^(-1)(1/(x^2+x+1))+tan^(-1)(1/(x...

If `y=tan^(-1)(1/(x^2+x+1))+tan^(-1)(1/(x^2+3x+3))+tan^(-1)(1/(x^2+5x+7))+.....` to nterms, show that `(dy)/(dx)=1/((x+n)^2+1)-1/(x^2+1)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|3 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise SOLVED EXAMPLES|7 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

tan^(- 1) (1/(x+y)) +tan^(- 1) (y/(x^2+x y+1)) =cot^(- 1)x

If y=tan^(-1)(1/(1+x+x^2))+tan^(-1)(1/(x^2+3x+3))+tan^(-1)(1/(x^2+5x+7))++ upto n terms, then find the value of y^(prime)(0)dot

If y=tan^(-1)1/(1+x+x^2)+tan^(-1)1/(x^2+3x+3)+tan^(-1)1/(x^2+5x+7)++ upto n terms, then find the value of y^(prime)(0)dot

If y = tan^(-1) ((1)/(x^(2) + x + 1)) + tan^(-1) ((1)/( x^(2) + 3x + 3)) + tan^(-1) ((1)/( x^(2) + 5x + 7))+ tan^(-1) ((1)/( x^(2) +7x + 13)), x gt 0 and ((dy)/( dx))_(x=0)= ( - k )/( 1+ k) then the value of k is

Solve: tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36))

Solve tan^-1(1/(1+2x))+tan^-1(1/(1+4x))=tan^-1(2/x^2)

(1+x^(2))tan^(-1)x*(dy)/(dx)+2=0

Prove that tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)((2x)/(2-x^2))

Solve: tan^(- 1) (2+x) + tan^(- 1) (2 -x ) = tan^(-1) 2/3

Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4