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Differentiate the following w.r.t. x: ...

Differentiate the following w.r.t. x:
`(x)^(logx)`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following w.r.t. x: (sec^2x)^(1//x)

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  2. Differentiate the following w.r.t. x: (x cos x)^x

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  3. Differentiate the following w.r.t. x: (x)^(logx)

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  4. Differentiate the following w.r.t. x: (logx)^(logx), x > 1

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  5. Differentiate the following w.r.t. x: x^(sin 2x + cos 2x)

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  6. Differentiate the following w.r.t. x: x^(sin x + cos x )

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  7. Differentiate the following w.r.t. x: (logx)^x

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  8. Differentiate the following w.r.t. x: (sin^-1x)^x

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  9. Differentiate the following w.r.t. x: (tan^-1x)^x

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  10. Differentiate the following w.r.t. x: x^(cos^-1x)

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  11. Differentiate the following w.r.t. x: (sinx)^(cos^-1x)

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  12. Differentiate the following w.r.t. x: (sinx-cosx)^(sinx-cosx), pi/4<...

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  13. Differentiate the following w.r.t. x: cos(x^x)

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  14. Differentiate the following w.r.t. x: (1+x)^(logx)

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  15. Differentiate the following w.r.t x (log x)^(cos x)

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  16. Differentiate the following w.r.t. x: x^(sinx) + (sinx)^x

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  17. Differentiate the following w.r.t. x: (x)^(logx) + (logx)^x

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  18. Differentiate the following w.r.t.x. x^(tanx) + (tan x)^x.

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  19. Differentiate the following w.r.t. x: x^(cotx) + (cosx)^(sinx)

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  20. Differentiate the following w.r.t. x: x^(cosx) + (cosx)^x

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