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

If `y = (x sin^(-1) x)/(sqrt(1 - x^2)) + "log" sqrt(1 - x^2)`, prove that `(dy)/(dx) = (sin^(-1)x)/((1 - x^2)^(3//2))`

Answer

Step by step text solution for If y = (x sin^(-1) x)/(sqrt(1 - x^2)) + "log" sqrt(1 - x^2), prove that (dy)/(dx) = (sin^(-1)x)/((1 - x^2)^(3//2)) by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)|94 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION XII)(LONG ANSWER TYPE QUESTIONS) |1 Videos
  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos
  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

int (x(sin^-1x))/(sqrt(1-x^2))dx

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

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

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

If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) , then show that (dy)/(dx) = x/(sqrt(1 - x^4))

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

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

Prove that: d/dx[sin^-1sqrtx]=1/(2sqrt(x-x^2))

If sqrt(1 - x^6) + sqrt(1 - y^6) = a^3 (x^3 - y^3) prove that (dy)/(dx) = (x^2 sqrt(1 - y^6))/(y^2 sqrt(1 - x^6))

If log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2) , show that (1 - x^2) (dy)/(dx) + xy + 1 = 0