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A differentiable function f defined for ...

A differentiable function f defined for all x > 0 and satisfies `f(x^2)=x^3` for all x > 0. What is the value f'(16) ?

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`f(x^2)=x^3rArrf(x^2). 2x=3x^2rArrf(x^2)=(3x)/2rArrf(4^2)=(3xx4)/2rArrf(16)=6`
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MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Give example of a function whose is continuous but not differentiable ...

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  2. If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then w...

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  3. A differentiable function f defined for all x > 0 and satisfies f(x^2)...

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  4. If f(x) =[tan^2x], what is f ' (0)?

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  5. If f(x) = (3x+2)^100 and f ' (x) = n(3x+2)^99 then what is the value o...

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  6. If xin((3pi)/4,pi) what is dy/dxfor y = | cos x | + | sin x | ?

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  7. What is the derivative of f(In x) with respect to x where f(x) = In x ...

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  8. If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?

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  9. Defferentiate tan^(-1) frac (2x)(1-x^2) w.r.t. sin^(-1) frac (2x)(1+...

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  10. What is the differential co-efficient of "tan"^(-1)sqrt(1+x^2-1)/x wit...

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  11. If y=at^2, x= 2at where a is a constant what is the value of (d^2y)/(d...

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  12. Is the function f(x)="sin"^(-1)(2x)/(1+x^2) differentiable at x=pm1?

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  13. Write the value of d/dx(sin^-1x+cos^-1x) for x in(-1,1).

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  14. Write the value of d/dxsec^-1(1/(2x^2-1)), for x in(0,1/sqrt2).

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  15. Write the interval in which the fuction f(x)=sin^-1(1-x) is differenti...

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  16. Write the value x for which d/dxsin(sin^-1x)=1

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  17. Write the value x for which d/dxsin^-1(sin x)=1

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  18. Write the derivative of sec^-1x with respect to x at x=-1/3.

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  19. Find the derivative of Inxa.

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  20. Write a logarithmic functions which is differentiable atevery point in...

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