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Find d/dx(sin^(-1)x)^(x^2)...

Find `d/dx(sin^(-1)x)^(x^2)`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. Let f(x)=e^(x)g(x),g(0)=2 and g(0)=1, then find f'(0) .

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  2. If x in(0,pi/2) then find d/dx(sinx).

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  3. Find d/dx(sin^(-1)x)^(x^2)

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  4. If f(x)=[x^(2)] then f(3/2)=.

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

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  6. What is the derivative of f'(lnx) w.r.t. x where f(x)=ln x.

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  7. Find the derivative of log(x)a.

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  8. If x^(y)=e^(x-y) then find dy/dx.

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  9. Examine the continuity of the function f defined by f(x)={[2x+1if x<1]...

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  10. examine the contiunity of the following functions at indicated points ...

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  11. Examine the contiunity of the following functions at the indicated poi...

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  12. Find the value of a such that the function f defined by f(x)={((sinax...

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  13. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  14. Examine the contiunity of the the following functions at indicated poi...

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  15. Examine continuity and differentiability f(x)={[xsin1/x,if x!=0],[0,if...

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  16. Test differentiability of the following function at the indicated poin...

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  17. Differentiate x^(sin^(-1)x w.r.t. sin ^(-1).

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  18. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  19. Find dy/dx for (x+y)^(cosx) = e^(x+y).

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  20. If 2^(x)+2^(y)+2^(x+y) , then find dy/dx at x=y=1.

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