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Differentiate the functions w.r.t. x. ...

Differentiate the functions w.r.t. x.
`(x cos x)^(x)+ ( x sin x)^(1/x)`.

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The correct Answer is:
`(xcos x)^(x)[1-x tan x+log (x cos x)]+(x sin x)^(1/x)[(x cotx+1-log(x sin x))/(x^2)]`
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NCERT TAMIL-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.5
  1. Differentiate the functions given in Exercises 1 to 11 w.r.t. x. cos...

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  2. Differentiate the functions given in w.r.t. x. sqrt(((x-1)(x-2))/((x...

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  3. Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (lo...

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  4. Differentiate the functions given in Exercises 1 to 11 w.r.t. x. x^(...

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  5. Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (x+...

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  6. Differentiate the functions given in w.r.t. x. (logx)^(x)+ x^(log x)...

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  7. Differentiate the functions given in w.r.t. x. (logx)^(x)+ x^(log x)...

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  8. Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (si...

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  9. Differentiate the functions w.r.t. x. x^(sin x)+(sin x)^(cos x).

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  10. Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (lo...

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  11. Differentiate the functions w.r.t. x. (x cos x)^(x)+ ( x sin x)^(1/x...

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  12. Find (dy)/(dx) of the functions. x^(y)+y^(x)=1.

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  13. Find (dy)/(dx) of the functions given in Exercises 12 to 15. x^(y)= ...

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  14. Find (dy)/(dx) of the functions given in Exercises 12 to 15. (cos x)...

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  15. Find (dy)/(dx) of the functions given in Exercises 12 to 15. xy= e^(...

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  16. Find the derivative of the functions given by f(x)= (1+x)(1+x^(2))(1+x...

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  17. Differentiate (x^(2)-5x+8)(x^(3)+7x+9) in three ways mentioned below :...

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  18. If u, v and w are functions of x, then show that (d)/(dx)(u.v.w) = (...

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