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If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^...

If `y=(x+sqrt(1+x^2))^n` then `(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. (d^(20))/(dx^(20))(2cosxcos3x) is equal to........

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  2. If y=x^3(log)e(1+x) , then y'(0) is equal to.......

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  3. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

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  4. f(x) and g(x) are two differentiable functions in [0,2] such that f"(...

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  5. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

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  6. If f(x)=xtan^(-1)x, then f'(1) is equal to

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  7. If f(x)=(log)x(logx) , then f'(x) at x=e is equal to......

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  8. If y=(log)(sinx)(tanx) , then (((dy)/(dx)))(pi//4) is equal to.......

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  9. If x^my^n = (x + y)^(m+n), then (dy/dx)(x=1, y=2) is equal to

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  10. Let f, g and h are differentiable functions. If f(0) = 1; g(0) = 2; ...

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  11. Find the derivative with respect to x of ((log)(cosx)sinx)((log)(sinx)...

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  12. Evaluate: intsin^(-1)((2x+2)/(sqrt(4x^2+8x+13)))dx

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  13. Let f(x) = x^2-4x-3, x > 2 and let g be the inverse of f. Find the val...

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  14. Let f : R -> R be defined as f(x) = x^3 + 3x^2 + 6x-5 + 4e^(2x) and ...

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  15. Suppose f^-1 is the inverse function of a differentiable function f an...

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  16. If y = y(x) and it follows the relation e^(xy) + y cos x = 2, then fin...

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  17. A twice differentiable function f(x)is defined for all real numbers an...

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  18. If x=2cost-cos2t & y=2sint-sin2t , find the value of (d^2y//dx^2) when...

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  19. Find the value of the expression y^3((d^2y)/(dx^2)) on the ellipse 3x^...

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  20. If sqrt(x^2+y^2)=e^(sin^(-1)(y/(sqrt(x^2+y^2)))). Prove that (d^2y)/(d...

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