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Fill in the blanks : d/dx [sin^-1 *(2x)/...

Fill in the blanks : `d/dx [sin^-1 *(2x)/(x^2 +1)]`=________

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JMD PUBLICATION-Continuity and differentiablity-Exercise
  1. Fill in the blanks : d/dx [sqrt (4x + 5)]=

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  2. Fill in the blanks : d/dx [cos^-1(sin x)]=

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  3. Fill in the blanks : d/dx [sin^-1 *(2x)/(x^2 +1)]=

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  4. State True/False : the derivative of [e^(e^x] is [e^(e^x]

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  5. State True/False : the derivative of [ e^{log(4x+3)} is 4

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  6. State True/False : the derivative of [sin^-1 x + cos^-1 x] is pi/2

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  7. If [x= a{theta - sin(theta)] and [y= a{1 - cos (theta)] find [d^2y/dx^...

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  8. Verify Lagrange's Mean value Theorem for the function [f(x) = sqrt(x^2...

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  9. Differentiate y with respect to x, where [y= tan^-1 { sqrt(1+sin x) + ...

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  10. find dy/dx, if [ sin^-1 {5x + 12 (sqrt(1- x^2)} / 13]

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  11. Differentiate [tan^-1 {2x/(1-x^2)}] W.r.t [sin^-1 {2x/(1 + x^2)}]

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  12. Differentiate [(log x)^x + x(log x)] w.r.t X.

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

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

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

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

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

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

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

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