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Let f(x)=e^(x)g(x),g(0)=2 and g(0)=1, th...

Let `f(x)`=`e^(x)g(x)`,`g(0)=2` and `g`(0)=1`, then find f'(0) .

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. Find the derivative of sin x^(0) w.r.t. x.

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  2. Differentiate sin^(-1)(2xsqrt1-x^(2)) w.r.t. x.

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  3. Let f(x)=e^(x)g(x),g(0)=2 and g(0)=1, then find f'(0) .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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