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If y = {x+sqrt (x^2 + a^2})^n, prove tha...

If `y = {x+sqrt (x^2 + a^2})^n`, prove that `dy/dx= (ny)/sqrt (x^2+a^2)`.

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JMD PUBLICATION-Continuity and differentiablity-Exercise
  1. Differentiate [(log x)^x + x(log x)] w.r.t X.

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  2. IF f(x) = [(3 + x) / (1+ x)]^(2 +3x)] find'(0).

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  3. If y = {x+sqrt (x^2 + a^2})^n, prove that dy/dx= (ny)/sqrt (x^2+a^2).

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  4. IF [x= a {(1 + t^2) /(1-t^2)] and [y= 2t/(1 -t^2)] find dy/dx.

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  5. If x= 3 sin t - sin 3t, y = 3 cos t - cos 3t, find d^2 y/dx^2 at t= pi...

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  6. Differentiate [x ^(tan x) + sqrt(x^2 + 1 / x)] w.r.t X.

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  7. IF y= x^x , show that [(d^2y/dx^2) -1/y(dy/dx)^2 - y/x = 0]

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  8. x= a sin 2t(1 + cos2t) and y = b cos 2t(1- cos 2t) , show that [(dy/dx...

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  9. Verify Lagrange's mean value theorem for the following function : [f(x...

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  10. f(x) = [(1-sin^3x)/(3cos^2x) ,if x< pi/2], [a, if (x= pi/2) if f(x) b...

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  11. IF [y{sqrt(x^2 + 1)- log {1/x +sqrt(1+1/x^2)}] find dy/dx

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  12. IF y =[log (x+ sqrt(1+ x^2))]^2 ,show that (1+ x^2) (d^2y) /dx^2 +x(dy...

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  13. Diff. [x^(sinx) + (sin x)^ cos x] w.r.t. x.

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  14. IF [log (x^2 + y^2) = 2 tan^-1 (y/x)] then show that , dy/dx = (x+y) /...

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  15. IF [y= (sin^-1) /sqrt(1-x^2)] show that : [(1 -x^2) (d^2y /dx^2) - 3x(...

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  16. If y= e^(a sin^-1 x) , [-1le x le 1]then show that (1 -x^2) (d^2y) /(...

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  17. IF [x^p y^q = (x+ y)^(p+q)], prove that dy/dx = y/x.

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  18. Differentiate tan^-1{( sqrt (1+x^2) +sqrt (1-x^2))/ (sqrt(1+x^2)-sqrt(...

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  19. If [(cos x)^y = (cos y)^x ] find dy/dx,

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  20. Differentiate the following with respect to x: [ sin^-1 {2^(x+1) 3^x} ...

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